Unless he's tangling with aliens or interdimensional imps that wear a costume identical to his own, Batman works with almost any type of villain. Usually, the Dark Knight functions best against foes that are human and psychotic, but that doesn't mean that he can't battle superpowered villains too. Although his rogue's galley isn't replete with metahuman antagonists, Batman has defeated more than his fair share of clay monsters, sexy floramancers, literal burning skeletons, and an immortal eco-terrorist. The character has tremendous range.
However, even though it's rare, Batman has another class of villain he pairs well against, and DC's animated film division is finally going to give it to him. Batman vs. almost any horror character works every single time. In the video linked above, you can check out the trailer for the new DC animated film Batman: The Doom That Came to Gotham, which features the Caped Crusader battling a host of unholy antagonists.