Here's what the BBFC have to say about their ratings:
12(A):
Theme
Mature themes are acceptable, but their treatment must be suitable for young teenagers.
Language
The use of strong language (eg 'f***') must be infrequent. Racist abuse is also of particular concern.
Violence
Violence must not dwell on detail. There should be no emphasis on injuries or blood. Sexual violence may only be implied or briefly and discreetly indicated.
Imitable techniques
Dangerous techniques (eg combat, hanging, suicide and self-harming) should not dwell on imitable detail or appear pain or harm free. Easily accessible weapons should not be glamorised.
Horror
Sustained moderate threat and menace are permitted. Occasional gory moments only.
and there was no sex, drugs or violence so those are no worries.
15:
Theme
No theme is prohibited, provided the treatment is appropriate to 15 year olds.
Violence
Violence may be strong but may not dwell on the infliction of pain or injury. Scenes of sexual violence must be discreet and brief.
Imitable techniques
Dangerous techniques (eg combat, hanging, suicide and self-harming) should not dwell on imitable detail. Easily accessible weapons should not be glamorised.
Horror
Strong threat and menace are permitted. The strongest gory images are unlikely to be acceptable.
To be honest, I think the 12 rating was perfectly acceptable. There was no blood (except stitching, and smeared against Joker victims' face paint); Two-Face was gruesome, but there was no emphasis on the pain his scarring caused him, and a lot of the more horrible violence (including all of the deaths) only occurred off-screen (Lau burning, Gambol face-slit, Wuertz being shot); there was one use of bad language (son of a) which is totally passable; the fighting was not bad compared to some other 12 films...
...I guess the most difficult part to digest would be the themes presented in the movie. It was dark, horrible, guns pointed at children and people forced to kill each other nasty. But whatever.