There's really nothing at all eccentric about our criteria, so you're likely able to make it with your common sense. The short version: as long as your writing is grammatically functional and your character is realistic, you won't have a problem. We're not out to make the application process difficult by any means.
In other words, a solid grasp on grammar, sentence structure, and the other goods. It will probably be most distinguishable in your writing sample, though the rest of the application should be similar.
2. Canon consistency
Pretty self-explanatory - you shouldn't contradict anything established in the books about the wizarding world. The application also shouldn't be anachronistic; since Chimera is set in the 1940s, references to the Beatles would be jarring.
Basically, the character should make sense, or believably exist as a real person, at least in concept.
In the best case scenario, we'd love to have characters that are more than a collection of adjectives and a picture. This applies especially to important characters. If you were to apply for Tom Riddle, for example, we'd probably require more insight than for a ghost.
p i t f a l l s
These are common pitfalls we've seen in HP apps before. Note that just because it appears here doesn't mean it's impossible to pull off, per se, but it's usually a red flag.
• A traumatic past that is completely overblown and unrealistically hyperbolic, often leading to a victimized complex. Bad childhoods are possible and definitely exist canon-wise, but try to exercise subtlety.
• Perfect characters should be avoided, as defined by those without weaknesses and with impossibly prodigious skills far beyond their age.
• Psychological disorders introduced as gimmicks to make characters unique, usually with portrayals that are inaccurate and handled awkwardly. Mental diseases have very serious side effects that impede everyday activities, and cannot be limited to cherry-picked symptoms.
• Flamboyant homosexuality is very rare in this era. While slash is all well and good, we also have to be realistic about the trends during this time, well before the cultural revolution and set in a much more conservative atmosphere. Deviant sexuality is not at all widely accepted, and emotions such as denial and shame are much more prevalent.
• Non-human characters should mostly be restricted to those listed on the canon list. As far as we are aware, Remus Lupin was the first werewolf to come to Hogwarts, so there shouldn't be earlier ones running around on the grounds. With the exception of Sanguini on the canon list, vampires are similarly restricted. As for half-Veelas, half-Giants (besides Hagrid), and other sorts, please PM the staff about the concept before you apply. We will be reluctant to accept them, as they are supposed to be extremely rare. Currently not accepting any non-human originals.
• Referencing other characters in your app should be avoided unless you talked to the player of that character beforehand. In other words, we don't want to see a girl claiming she is the granddaughter of Dumbledore.