I see so many people complaining how Akali can't carry or she is bad and when I look them up they're like silver or gold.
1. Akali is not bad. Either said player does not have the mechanics to perform and then carry or they fail to play Akali properly overall.
2. For low elo I maintained a 96% win rate from bronze to gold 1.
3. High elo I am currently at a 68% win rate in diamond 3/diamond 2.
This is not a flex. Yes it's a one person statistic, but it's not an anomaly. I have played over 500 games of Akali. I know every matchup. I know how to carry. When one gains said knowledge Akali becomes incredibly easy to not only solo kill laners but also carry the game.
People argue either her teamfight is poor or her laning phase is awful.
I've played against challenger mid/top laners: rovex, erick dota, boxbox, wingsofdeathx, I don't lose lane.
Learn to play passive. Doran's shield regen is king. Save shroud.
"Akali's teamfight is awful!"
I initiate. You are building Akali incorrectly.
1. Conquerer. Sustain within a teamfight, good damage.
2. Trinity force first item. Good powerspike with sheen, innate tankiness, very good stats and powerspike when completed
3. Steraks and Death's dance, more innate sustain and tankiness, cdr
4. Generic tank items (GA, Spirit Visage, Randuins, Dead man's, etc.) Building each depending on enemy team comp and how far ahead I am.
"Akali's laning phase is awful!"
I have yet to be solo killed. Learn when to take teleport. Learn when NOT to fight. Learn to ward. Learn when to roam. Learn how to freeze mid lane and when to call the jungler to break a freeze or help push and then reset.
Kills are not of importance. Farm until sheen / phage / boots and double kill bot lane.
The only matchups I have had trouble with are Veigar.
I ban Veigar every game.
Matchups:
Ahri: Rush mercs, dodge charm within w, if her ult is down and you dodge charm should be an easy solo kill. Look to play a generally passive lane, don't need to kill her and don't die or she will snowball. Can duel with mercs / trinity force. Call jungler if she burns her ult.
Anivia: One of the only matchups I go tiamat, basic afk farm lane, if it's a bad anivia player look for solo kill else rush tiamat and mercs and afk farm.
Annie: Easier matchup, trade with shroud and q + auto spam, can all in with null magic + ult + phage at 6 for an easy solo kill.
Azir: Annoying matchup, he will AFK shove, do NOT all in if near his turret as he just ults you, let him push you in and farm under turret. Call jungler. Can solo kill with null magic + phage with 6. Notice if he has barrier.
Asol: Incredibly easy matchup. If he's decent he shoves early levels, just farm under turret. Kill at 6 with sheen or phage.
Brand: Easier matchup. Save E for dodging his q or W, rush mercs and all in once his Q or W are down.
Cassiopeia: Medium, she can cheese you with q + e spam lvl 2 careful for that. Notice phase rush, cleanse, barrier, etc. No need to solo kill, play passive and look for jungler ganks and roam.
Corki: Harder matchup, good corkis with fleet will spam auto you, dshield start and play passively (Q farm if they're decent) Can solo kill at 6 with jungler or sheen.
Diana: Easy matchup. Melee champion so spam q. Dodge q by walking towards her and away, Basically moving the opposite direction in which the q lands, hard to explain. If she lands Q she can burst you at 6, just shroud or E-dodge.
Fizz: Q spam melee champion, can burst you at 6, rush MR (I often go hexdrinker + ruby crystal in this matchup for tankiness) and look to all-in once his e is down, can dodge his q/e with e, save shroud for his ult.
Galio: Nobody plays Galio mid, but just Q spam, rush mercs, can't solo kill because he's galio, look to roam.
Heimerdinger: Dodge
Irelia: Incredibly easy, dodge E with your e or sit in shroud, q spam and if she uses her E can all in with ult. Remember her stun CD.
Kassadin: Somewhat difficult, rush hexdrink / early MR, Q spam him until 6, try to get JG gank pre-6, look for solo kill Pre-6 as well. I almost always take teleport in this matchup.
Katarina: Fun matchup, purely skill matchup. Better player will win. Rush null magic, phage, play around her daggers, she can all in at 6. Save ult to cancel her ult if need be, if Akali initiates on her she will most likely lose in a fair fight.
Leblanc: Save E for her w, rush early magic resist, hard to solo kill with W / passive but if her CDs are down Akali will win in the 1v1 if played perfectly. Generally play lane passively, I usually take teleport.
Lissandra: Boring farm lane, She can't kill you and you can't kill her. I sometimes run tiamat, take teleport and AFK shove and look to roam. Rush mercs.
Lux: Another annoying matchup, stay semi-far back to dodge E, if you get binded you will die. Save E for dodging Q if need be, can trade easily with q/passive spam if you can dodge.
Malzahar: Rush early QSS and he can't do anything. Take teleport. Somewhat hard to kill with QSS Tax but prevents death, look to roam once he resets.
Neeko: Rush MR, save ult for escaping her ult, don't stand behind minions to avoid empowered E (stand towards the left and right sides of casters and adjust position accordingly)
Orianna: Rush some early MR, can duel early as well with her long cooldowns, Good Orianna players will punish, take teleport and lose farm if need be, can kill at 6.
Ryze: He will AFK shove early, try to look for JG gank, take teleport and rush mercs. Don't stand near minions as to avoid e, notice when he is oom and then shove, if he doesn't have teleport you win lane.
Swain: Easy matchup, trade around his E cooldown. If he ults either continue fight if you are stronger, else ult out. Rush mercs.
Syndra: Rush early MR, take teleport unless you have confidence in your solo kill abilites, play passively and dodge q's (good syndras will Q you when you are looking for last hits, play around it) play around her stun.
Sylas: Annoying matchup, rush mercs, play around his stun, hard to all-in with him stealing Akali ult and the heal. Generally just AFK shove and ignore him, look to roam or get a jungler to gank.
Taliyah: She AFK shoves and then roams, take telport, tiamat if you want. Rush early MR and all in once her e is down.
Talon: Rush early armor, play around his W cooldown, if you get hit by both W procs either shroud or E out as bleed does an insane amount of damage, trade around shroud and his W cooldown, notice when he roams and either shove and spam-ping teammates or look to follow.
TF: Take teleport. If he is looking to roam (obviously walking towards a lane whilst under vision ping it) My favorite mechanic is you can follow his teleport with your E if he is stupid enough to ult within vision. TF has bad damage early game, look for early solo kills with sheen / phage.
Veigar: I ban this champ every game. Cage is broken. Dodge.
Vel'koz: Play semi-passive, Take teleport if you want. To effectively dodge Velkoz Q walk towards the Q such that it will activate behind you. Play around his E cooldown, use e to dodge and or gap close. All in at 6. Notice barrier.
Viktor: AFK Farm matchup, can usually all-in / duel pre 6, he has decent DPS at 6. I usually rush MR. Take teleport.
Vladimir: He loses early, scales with CDR. I take teleport and rush MR and then afk shove and look to roam. Hard to solo kill / gank. If he has his empowered Q just back off.
Xerath: He AFK shoves if he is decent, learn to dodge xerath q. Don't stand still. I take teleport and rush MR and then all-in with said MR. Notice barrier. Play around E cooldown, utilize W to more effectively dodge by standing on far edges of shroud.
Yasuo: Easy matchup. Q spam the melee champion. Notice windwall cooldown, can all-in at pretty much any time. He can kill with shroud down so take caution in that. I don't usually go early armor and I take ignite.
Zed: Annoying matchup, try not to get solo killed and rush early MR, I usually take teleport and let him shove me in, dodging his double q with my E, hard to solo kill. Potential once his shadow is down due to long cooldown.
Ziggs: Easy matchup, play around his W and q spam him with shroud up, can e towards him and q spam as well. All in at 6. Take teleport in need be. Notice barrier or heal.
Zoe: Rush mercs!!! Take cleanse if you want. I usually take teleport and hide behind minions, can bait out her e with shroud and hiding on edges, if her E is down all in with ult.
General playstyle:
I only play bruiser akali because of her insane teamfighting and sustain and innate tankiness. With conquerer, death's dance, and more healing from the domination tree she has a lot of healing and sustain within a teamfight and innate tankiness with sterak's, 40% cdr, and MR and or armor. She has very good dueling capabilities late game and I almost always initiate the fight with Flash --> Ult --> q --> shroud.
Laning phase:
In most of my matchups I take teleport. Ignite is not needed for a solo kill, although I run it in easier matchups, however winning lane can be done by knowing when to freeze / push / teleport back. And or fighting on that teleport back with an ult all-in when the enemy hasn't bought yet. Notice what items the enemy has.
I usually either push the wave if the enemy mid laner is garbage with auto / q spam on the entire wave or if they are decent I last hit with q and ignore them until levels 4-5. At this point I use my E to E towards them and q + passive +shroud MS + q auto and then backing off in the shroud. Q spam poke even on ranged matchups is what wins you the lane. Ranged matchups will poke you out levels 1-3, play passive and wait for 6.
Doran's shield is incredibly important for sustaining within a lane, you can go from chunked back to full within a minute or so just by last hitting with Q and playing passive. Losing farm is not a big deal, we can outplay with roaming, using teleport, and trying to solo kill at 6.
With melee matchups we spam q and passive poke an then shrouding when they come in. Melee matchups are very easy to gank with a jungler, initate with ult and then putting the e onto them for an easy kill.

Solo Kill Combos:
Basic Trade: E --> Q mid E --> Empowered Auto --> Q --> run back --> shroud --> empowered auto --> all in with ult or leave
Solo kill: Flash --> Ult --> E them whilst microstunning --> empowered auto --> q --> shroud --> empowered auto --> ult2
Execute combo on low health enemies: Empowered auto --> Q --> ult in quick succession.
E tips: Can be used to get over most walls, dodge abilities, going for a trade / execute kill and then e'ing back onto a minion or to shroud to get away, can be used as a powerful juking ability (think leblanc's w) and putting it on shroud or a minion and walking the opposite direction and then e'ing to safety. Learn to use E and 2 empowered autos, in the sense you E into a wall (not jumping the wall) as to reduce distance, empowered auto, e again, and empowered auto.

When to roam: If you know your laner is backing or wants to back (oom, hasn't bought yet, etc.) shove wave. At level 7 two q's will kill back minions so it is easy to shove move laners in, and then roam bot. Almost always only roam if you have boots as without them you are incredibly slow.