Judge Style

Fun: In my opinion, the most important basic requirement for a high fun level is an appropriate difficulty – not too easy, not too hard. This doesn’t mean already that it needs to be challenging all the time – if the level conveys a kind of joyful or strolling-around atmosphere, it’s fine. The difficulty of a level must fit its intention. If there are challenges, they should be interesting, it gets annoying if you just jump on detached falling logs all the time, and stuff like random pipe mazes is even more terrible. Graphics and other stuff also influence the fun factor – if the graphics are just horrible, I quite don’t care about the gameplay even if its great. Fun also means atmosphere, the feeling to be abducted into the LDer’s own little world. Btw, minigames can also be fun if they introduce something new or uncommon.

To get many points in fun, here's what you can do:
Make some challenges that are thrilling, exciting or just simply unique.
Don't save coins throughout all the level, except if there must be really no coins for gameplaywise reasons.
Make something that makes adrenalin shoot through my blood. I love chase scenes (if executed well) and fast wing cap flights.
Various ways to finish the level, e.g. a special red coin/silver star challenge. But don't make it too hard, else it will simply be ignored.
If you make an easy level, don't make it way too easy, at least add some neat touches of platforming.
As noted above, also take care about creating a good atmosphere.
To avoid getting a low score in fun, avoid this:
Unsufficient playtesting. This can mean that challenges are too hard/almost impossible, or that there are gamebreaking bugs making it possible to bypass obstacles in an unintented way. (however, bagatelles like e.g. a malfunctioning pipe fall under "Other" and won't reduce the Fun score)
Boringness. If I have nothing to do while playing, I'll probably never play the level again. But this doesn't mean the level should be long. Small levels can also be fun as well. However, if you wanna go the extra mile, quantity is indispensable.
Spamming enemies. If I get hit one time after the other by bullet bills, ghosts, skelegoonies etc. without purpose, I'm annoyed.
If there are heavy flaws in the other sections (e.g. cutoff), it also damages the enjoyability of the level.
4-: That just didn’t work well, it lacks of effort, it’s not interesting and not worthy to play it again. Platforming wasn’t existing or it was too straight-forward and predictable. Or it was just way too hard (*cough* Celestial Trials *cough*).
4 - 6: There were a few interesting rudiments but it still needs a lot of improvement. Platforming is still exiguous or the difficulty is too high.
6 - 7.5: This is mediocre. Decent, but not stunning. The LDer has shown he has requirements to do well. It can be good if more innovation is added.
7.5 - 9: This is were it starts to make fun, and where it’s definitely worthy to play it again. Interesting platforming or challenges, a comprehensible level structure, and difficulty also goes as well.
9+: Absolutely amazing, I want to play it again and again. Everything is cleverly elaborated and well-connected together, the difficulty is perfect, graphics etc. also support it, there’s almost nothing you can improve.

Graphics: Great levels are artifacts. There’s no way to deny this. Graphics is what makes the atmosphere of a level and the feeling behind it, like denoted above. Tiling should be interesting and variable most of the time, but sometimes it can also be a bit drab if there’s a good reason behind it, e.g. how looks a sunken ghost ship with mansion tiles and brown bricks arranged in a chessboard pattern? Quite stupid :P "Cutoff" can also be good if it's covered up and arranges well with other tiles (thinking of Dorams “Impossible Treasures”). Generally, the best way is to make your tiling unconventional, but even more good-looking. Next, décor. It’s not important to use as much décor as possible, it’s important to use it in an appropriate way, meaning: Décor where there needs to be décor. If it’s exaggerated, it’s not good (and it also causes lag and loading time). But if décor is missing where it’s needed, it causes a boring or sad atmosphere. I don’t think there are universal principles about to use which plants in which regions, it also applies here: unconventional, but even more good-looking. (But if you decorate conventionally, it's also okay).

To get a high score in Graphics, do this:
Adjust the graphics to what the level is supposed to be.
Variated tiling. It enlarges the code, but not the loading time (I suppose). Work with various colours, especially in factories/castles etc.
Some kind of slopes or vertical ascensions are good as well.
DECORATION. The most important point IMO. It's needed almost everywhere, but also don't exaggerate it. Don't be afraid of using décor only because of the god dammit loading time. If your level takes long to load only because you've used décor plenty but wisely, I try to be merciful on that.
When having these things in your level, you're almost sure to land in the lowest or second lowest tier, except the rest is amazing:
(uncovered) CUTOFF. Do I need to tell more? Well, the only exception is using jungle ground tiles in a desert to indicate quicksand.
LACK OF DECOR WHERE THERE NEEDS TO BE DECOR. Good tile mixtures can not only make up for a good atmosphere. Without décor, most places look rather barren, except for maybe factories or airships.
Monotonousness. If there's nothing but red and blue bricks in a level, it's just terrible.
1.5-: Horrible graphics, reminding me of crappy portal levels. Stupid cutoff and/or drab plainness, no innovativeness, no atmosphere.
1.5 – 2.75: It’s not that horrible, but still rather boring and uninteresting. It still lacks variation and/or good décor use.
2.75 – 4: It’s maybe not that boring, it has some variation, but not much innovativeness, there are still many possibilities to improve it. Décor could also be used better. When approaching the 4 region, it means you’ve already done a good job, but you should still try to create more shapes and more atmosphere.
4 – 4.75: Very pretty tiling and also quite good use of décor, but it still has some minor flaws and there’s something missing to make it memorable and unique. Nonetheless, you’re showing a great graphics style, I’m willing to see more.
4.75+: Your graphics are excellent, everything fits well together, everything looks awesome. It creates a wonderful atmosphere and has a high or even very high artistic standard. All I can say is “Bravo!”.