I've seen plenty of animated 'art films' that employ an atonal language. And of course, even more mainstream films may have single tracks that venture into this territory. But I have to think a little bit about any titles.
Does Leonard Rosenman's THE LORD OF THE RINGS count?
How are we defining "atonal?" That term is thrown around a lot.
Good question. Dictionary.com helpfully describes "atonal" as: of, pertaining to, or marked by atonality.
Then again, I've often seen "Alien" described as an atonal score, despite having a good amount of melodic content, so maybe that's a good example: any score with a decent amount of non-melodic material.
One of my favorite animated scores, Kenji Kawai's "Ghost in the Shell", features atonal work:
And while I'm not as familiar with the score for "Akira", I seem to recall some rather cacophonous atonal material featuring there.