Bat Quirk gives it's user bat features like wings on his arms, fangs, pointed ears, etc. The Quirk allows its user to run at high speeds, as well as the ability to fly. However, this is only seen when Bat Villain was under the effects of Trigger, so the capabilities of the Quirk under normal circumstances are unknown.
After the Villain Factory turned him into a Next-Level Villain by modifying his body and enhancing his Quirk with more Trigger, his whole body became more bat-like, in addition to improving his physical abilities. His sense of smell improves and can detect a person's trail over long distances. His flight capacity also improves exponentially, being able to fly at great speeds. Bat Villain also acquires more strength, being able to capture a person with his claws and take him flying.