Everybody Hates Hades: Chernabog was a black god, but wasn't evil as a pre-Christian Slavic deity. Subverted as Walt said he was meant to be Satan anyway, and in the roadshow version, Deems Taylor identifies him as such.
Evil Is Burning Hot: Chernabog covers himself in fire near the end of "Night on Bald Mountain".
Slasher Smile: When he really liked his final transformation of his transformed minions
Villain by Default: Did Chernabog actually do anything inherently wrong? The answer - no, he did not, because he left no lasting damage and disappeared without having harmed anyone - apart from some demons perhaps. He summons an entire legion of demons, ghosts and otherworldly monsters so he can basically have a rave.
It is implied by Walt and Deems that he has done many crimes against God, so it is possible that he has harmed millions of lives before being sealed in the mountain. It's also possible he's enslaving and torturing the demons ad ghosts he summoned.
Big Good: Against the Firebird's Big Bad, it seems a very dominant force of nature in a positive way, whereas the Firebird enforces nature's power in the negative way. In the alternate ending, it even becomes the sun (or perhaps sunlight).
Adaptational Villainy: The Firebird of the original ballet the song originated from was actually a helpful creature that aided a prince to defeat an evil wizard. This Firebird on the other hand is a creature of pure destruction.
Evil Counterpart: To the Nature Sprite; she embodies life and nurturing of the world, while the Firebird brings only destruction and death. The commentary prior to his segment acknowledges this by calling it "a tale of life, death, and renewal," with the sprite representing life and the Firebird representing death.