Earth Prime Batman is just a man in a bat suit but on Earth-43 AKA Nightmare World, he’s a vampire! Batman meets Nightmare Batman in Infinite Crisis: Fight for the Multiverse #30. He travels to the eerie Earth to track down mysterious devices known as Earth Engines, which have been hidden on Earths across the Multiverse by the godlike Monitors.
Batman is escorted by Nightmare Robin, a vampiric version of his son Damian Wayne. They are attacked by dhampyre bats, the hybrid offspring of vampires and humans. Batman uses ultrasound to repel them but Robin warns him too late that he will attract something even worse. The chapter ends with Nightmare Batman looming over them. The creature gives him thorough thrashing in the following chapter.
Nightmare Batman was turned during a final showdown with his archenemy Ra’s al Ghul, whose immortality was due to vampirism rather than the Lazarus pits. Batman maintained control over his hunger until he killed the Joker and devolved into a wild animal.
A vampire Batman was first introduced in Batman & Dracula: Red Rain. This Batman was turned by a rebellious disciple of Dracula. He also succumbed to his condition after feeding on the blood of the Joker.