PoFV opinions

First let me point out that these are only my opinions. I've tried to outline the strengths and weaknesses of the characters and what their play styles are like. If I didn't comment on a character's matchups it's because I don't know it well enough or I think it's irrelevant. The order of the characters is vaguely based on tiers, at least as I thought of them a few years ago.

-Marisa-
Marisa's charge attack not only instantly destroys spirits, but causes them to explode as if they had been activated. This allows her to easily set off chain reactions anywhere on the screen without the need to rely on her scope. She generates more energy than other characters, and thus can cast spells more often. Her high unfocused speed is great for macrododging and synergizes with her laser, which can be swept across the screen. Marisa can also make very good use of level 1 invincibility frames due to her fast charge and movement speeds. Altogether, these give her excellent survivability. Offensively, her lasers suffocate the opponent and cannot be cleared by any means, eventually producing near impossible situations with brutal frequency. In a late game spell war, Marisa is probably the strongest character in the game.

Matchups: I don't think Marisa has any bad matchups. Reimu and Youmu can give her trouble in the early game, but once the rank is maxed out and spells are being cast constantly she should have the advantage over them.

-Youmu-
Good movement speeds. She can be very slow or very fast at will. The sword has little cooldown, so it can be used repeatedly despite her slow charge speed. With that speed, the bullet clearing effect, and the invincibility frames that come with all charge attacks, she can easily cut through situations that no mortal should be able to dodge, and she can do it very often. The dead souls suffocate the opponent much like Marisa's lasers (though they can be cleared away), her spell attack is long lasting (so it cannot be totally countered by the opponent's spellcasting), and the boss summon uses movement restricting patterns that are completely devoid of pellet bullets.

Matchups: Reimu forces her to the bottom, which exploits her lack of reach and makes it hard to start combos. Further, Youmu needs to be very careful with her movement during her charge attack. In order to properly defend herself with it, she needs to move upward while the sword is active, but if the aimed bullets from Reimu's spell target her just as she does this, they'll fan out behind her and prevent her from backing up again. Often this means you have to use the sword without moving vertically which dramatically reduces it's effectiveness. These make Reimu a very uncomfortable opponent in the early game. I think as time goes on and you begin relying more on spells and less on the sword the matchup evens out, but I'm not entirely sure of this.
Marisa seems to be pretty even with Youmu until very late in the game, where Marisa gains an advantage. You will reach a point where you cast one spell after another, and in order to buy yourself enough time to do this it's important to use the invincibility provided by the previous spell to misdirect the pellets to one side for as long as you can, then return to a safe spot between the lasers at the last possible moment. Because Youmu is slowed when she casts a spell, the distance she can cover while invincible is reduced, which makes dancing among the lasers like this more difficult. And on top of this her charge speed is of course very slow.
Other characters who might be strong against her are Eiki and Medicine, but I haven't seen enough of these to judge. Other than that, Youmu should have a very easy time against all the other characters.

-Reimu-
She's powerful because of her level 2, which limits the opponent's movement and spawns over a long period of time, meaning it cannot itself be entirely countered by a level 2 from the opponent. However, she faces extremely fast bullets constantly as they are returned from her own spells (speed is retained when bullets are reflected). Her movement is slow, and her scope is slow to expand. The charge attack is useless. These make surviving with her somewhat difficult. Overall, she's unremarkable in every way except for her spell, which is by far the best in the game and singlehandedly makes her a high tier character.

Matchups: Several characters seem to have the potential to be close to even with her, including Marisa, Youmu, Eiki, Komachi, and even Medicine. Precisely who is favored, and how strongly, in these cases is not really clear to me.

-Komachi-
Her awesome scope and auto-targeting charge attack give her a lot of freedom. She can essentially start a combo at will, from anywhere on the screen. She's not obligated to chase the fairies and spirits around to maintain her spell points, and so can pay more attention to dodging. Her spell is not very dangerous, but neither does it feed the opponent much energy, and since most characters' spells are basically free energy for the opponent anyway, this is actually pretty good. Her Extra attacks are great. They constantly cover the opponent's screen with random bullets, forcing them to the bottom. They're especially effective against fast characters who like to macrododge since they cover the whole screen evenly.

Matchups: She is at a severe disadvantage against Youmu, but can otherwise hold her own against the other high tiers.

-Lyrica-
Lyrica's scope is similar to Marisa's but is much harder to use due to her slowness. Her charge attack also only shoots straight forward and due to the fact that it stays in place it cannot be swept horizontally in the hopes of hitting an exposed fairy. This lack of coverage, again coupled with her slow movement, makes her extremely dependent on her scope to start chains, and her scope is just not very good. She also has rather slow charge speed. Her saving grace is her offense, particularly her spell. It covers a huge part of the screen and continues spawning over a long period of time, becoming an omnipresent threat much like Youmu's. Her boss and extra attack are also solid.

Matchups: Compared to other high tiers, she's held back by lackluster defense and feeding a little too much energy. I don't think she has any notable interactions with other characters and performs as you'd expect.

-Eiki-
Great movement speeds, scope, and charge attack. Her boss is also pretty good. Her extra attack "clones" existing bullets on the opponent's screen by firing a special, faster bullet in the same trajectory. Because the speed is determined by the original bullet, this is more effective against characters whose spells use fast bullets (Yuuka, Reimu, etc.). It's less effective against fast characters because pellet bullets are loosely aimed and thus the Extra attacks they spawn will tend to all fly in one direction and can be macrododged. Eiki's critical weakness is her spell. It's totally nonthreatening and every apparent pellet it creates is actually 2 or 3 pellets stacked directly on top of each other. All this does is feed the opponent tons of free energy.

Matchups: She's a character I'm a little unsure of. She loses to Marisa, and may struggle against Komachi and even Lyrica as well, but she seems like she can do okay against Reimu and Youmu. I'd like to see more high level games with her.

-Medicine-
Nice speed and scope, and her ability to pass through spirits is sometimes useful. Her charge speed is kind of low and her charge attack sucks. Her spell, much like Eiki's, does nothing but feed her opponent. Her extra attack is terrifying and its effect stacks, eventually almost freezing the enemy in place. Unfortunately they will usually have lots of energy to save themselves and the absence of an Extra attack that is directly lethal becomes really apparent as they have nothing to worry about but pellets. She's more effective against characters who have weak charge attacks, whose spells use fast bullets, and who are forced to stay focused for a long time in order to activate spirits, since this furthers their slowness and deprives them of fairy spawns.

Matchups: Of the characters with legitimate potential, she is probably the most unexplored.

-Yuuka-
Her boss, spell, and Extra attacks give her a decent offense as they force the opponent downward, but her defense is ruined by her slow movement. She has a hard time getting high enough on the screen to clear a decent area with her spells, and she's terrible at misdirecting and macrododging. This is a big problem because the number of pellets she creates tends to push the game toward a spell war, and she's just poorly equipped to handle that. Her offense also suffers from this as its main strength (trapping the opponent and pushing them down) starts to fail completely and the other player will actually stay very high on the screen with ease. Even her normally powerful boss is bad at preventing this.

-Aya-
Her focused speed is uncomfortably fast. Her spell and Extra attack aren't individually terrible but play exactly the same role, so as long as the opponent carefully moves in one direction they have very little to worry about. Still, her offense can be okay when the game picks up, especially when her boss is present since this makes it very hard for the opponent to move up. Her big problem is her defense. She has a hard time micrododging and gets tons of fast bullets continuously sent back at her from her spells.

-Reisen-
Good defense, terrible offense. Her spell creates too many bullets. She should only win against characters with slow charge speeds who cannot keep up with the all out spell spam that will inevitably ensue. Reisen herself is well equipped to deal with that situation, with her good scope, charge speed, and charge attack. Even then, between skilled enough players, a single round with Reisen in it can easily take a half hour or longer, regardless of which player theoretically has the upper hand.

-Cirno-
She's fast and has an okay scope. She charges a bit slowly but this doesn't matter too much. Her spell attack creates a simple ring of bullets, then freezes all bullets on both players screens (with the exception of a few character's extra attacks, including Cirno's), randomly changes their directions, then sends them all moving at once. The original speed of the bullets is not retained. Additionally, some non-pellet bullets on Cirno's screen (not the opponent's) will degrade into pellets, allowing them to be reflected. Her boss is very weak and her extra attacks are nothing special. Thanks to the freezing effect of her spells, Cirno has excellent defense and terrible offense, as her spells essentially help the opponent just as much as they help her. She's like Reisen but even more extreme.

Matchups: A very strange character. She's never played seriously, but from my experience I would say she has favorable matchups against Merlin, Lunasa, Tei, and Sakuya. She's also pretty even with Reisen, Mystia, and Yuuka. Cirno has essentially no offense, but she also shrinks her opponent's offense to virtually nothing as well (as long as it's not too strong in the first place). From there the game revolves around avoiding even the slightest risks as consistently as you can. Cirno is fast and has decent charge speed and scope. Characters with bad defense, awkward scopes, etc. cannot minimize risks as well as she can and so in the long run will lose to her. On the other hand, she's at a disproportionately extreme disadvantage against high tiers because their offense is so strong Cirno can't nullify it, and most of them have better defense than her too.

-Merlin-
Her movement, scope, and charge speed are all very slow. The scope is essentially Lyrica's but horizontal, and her charge attack shoots horizontally as well. Her basic shots do not spawn from the center of her sprite but rather from two points to her left and right. The shots from the right fly diagonally left and the ones from the left fly diagonally right, crossing each other's paths a short distance in front of her. If she hugs a wall the shots that should be spawning from off screen will simply fail to appear. Thanks to her scope she has difficulty dealing with spirits unless she stays focused for long stretches of time, which of course slows her even further and limits the fairy spawns on her screen. Offensively she's pretty good. Her spells last forever and limit the opponent's movement while her extra attacks send big bullets all over the screen. Her boss is also fairly strong.

-Lunasa-
While her movement and charge speeds are good, her defense is still a bit low thanks to her awkward scope and three-way shot. Her offense is likewise nothing to write home about. Her spell is so slow it hardly matters at all. Her extra attacks are okay for limiting the opponent's space, but are again very slow and can be easily streamed much like Aya's. Her boss is also unimpressive, with one attack in particular that's just free energy for the opponent.

-Mystia-
Defensively, she's not bad. Good speeds, fast scope, and an acceptable charge attack. Her offense however is miserable. The spell takes a thousand years to appear and even once it starts to move the bullets are slow. You might think at first that its slow appearance would make it somewhat resistant to being cancelled by the opponent's spells, but there is actually a single "generator" bullet (the bird-like thing) that spawns all of the others, and when that gets cleared the whole spell fails to appear. Once the game picks up the generator bullet will invariably be cleared away every time before the spell does anything at all. Her boss and extra attacks all behave similarly. Everything's just way too slow.

-Tei-
Fast while unfocused, quite slow when focused. Charge speed is excellent. Her scope is slow and poorly shaped (much like Merlin's), her charge attack is terrible. While slow focused speed is normally ideal, it's a rotten combination with slow scope speed, so spirits become a much greater nuisance than they would usually be. Her extra attacks aren't garbage but aren't very good either. They move too slowly to really accomplish anything. Her spell has barely any bullets and on top of that is easily cleared away before it does anything. The boss is pretty wimpy and has a pellet attack that's basically free energy for the opponent. Her ability is passable; it allows you attempt a level 2 rather than bombing even in very risky situations knowing the bomb will save you anyway if you get hit. Altogether her offense is pathetic and her terrible scope cripples her defense.

-Sakuya-
A single movement speed. This is strictly a weakness. Too fast for precision, too slow for anything else. The scope is awkward. The charge attack is even more useless than Reimu's. She is subject to a strange glitch; her time stop ends the bullet clearing effect of her spells. The result is that both the level 2 and level 3 clear the same area on her field, and this area is smaller than the area a normal character's level 2 would clear. Additionally, should you cast a level 2 just before an automatic level 3 occurs (through spell points reaching 500k) the time stop will cut it short instantaneously, and it will clear no bullets at all. The time stop can also toy with enemy spells, causing bullets which should have spawned over time to spawn all at once (for instance, Aya's spell can become a blanket across the whole screen). I will call this a weakness as it can lead to unpredictable things, though arguably it could be advantageous in some cases. Her spell itself is not threatening to the opponent. It spawns very few bullets, and they appear all at once. This makes it easy for the opponent to clear it away with their own spell. In fact it can often be cleared by a spell that was cast before the bullets even appeared. The knife rows can limit the opponent's movement but are very slow and become a non issue as spells are cast more frequently as the match progresses. The boss summon also uses slow, simple patterns.

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-General thoughts on movement / positioning-
There is a golden rule in shmups, or at least in ones where stuff tends to be aimed at you. That rule is "never stand in the same place you want to be in the near future". If you are waiting for the fairies to reach a certain position before you destroy them, do not wait in the spot you'll need to be in when you shoot.

Misdirection and macrododging are everything in this game. By hugging the wall and then moving to the center before the pellets engulf you, you can simplify a lot of the dodging you need to do. When misdirecting to the sides the higher up you can get the better, but beware fairies spawning into you. (These are the unsung cousins of ass fairies, even more bullshit, unfair, and evil.)

Never idle in the middle for no particular reason, especially after casting a spell. After a spell you should think about where you will need to be in the future, move far away from that destination, and then macrododge toward it such that you arrive on time.

Usually you should postpone the destruction of the fairies as long as you can, but sometimes you need to recognize when it's better to destroy them sooner. Fairies that overlap don't give you any greater coverage, and fairies in the middle of the screen will clear more than fairies near the edges. Following the big line of downward curving fairies to the bottom can sometimes put you in a bad position.

Ass fairies are a big fuck you from the game not just because they might ram you, but because they are near useless for chains. Whenever they appear get ready to endure some tougher than usual dodging for a while.

Lily White suppresses fairy spawns, so when she appears understand that what you have on screen at that moment is what you have to work with and plan your movements accordingly. (i.e. don't kill the fairies too soon.)

Never be too sure that your shots will kill their target. The fairies in this game exhibit a freakish resilience sometimes and you'll need to be prepared for what happens when they don't die when you thought they would. (I have a theory that there is an unexpectedly high penalty for not having both shots in a "set" hitting the same target, but I haven't tested this.)

Bullet Doppler! Move upward while firing to make your shots more compact so that they all hit the same fairy.

Holding focus suppresses fairy spawns, so try not to focus for long stretches of time. Focusing frequently and intermittently is okay. (Could explain exactly how this works but I don't think it's too important.)