If you're having difficulty with Black Cat, remember to not bother with healing. If you begin to, Black Cat will seize the opportunity and strike.
Black Cat is defeated with a combination of Web Zips (
), and well-timed dodges (
). Expect to hit Black Cat no more then four times before a dodge is needed. After she takes enough damage, she will run away to another part of the museum. Find a line of direct sight to zip to her and lay into her again. You'll know the fight is over once Black Cat waits for you in the middle by the mammoth skeleton. Once you Web Zip her again, Black Cat is done for.