Even if you ignore all that, Shauner. The sudden amazing fighting and athletic abilities, the expert handling of a whip, the love for milk, even in a movie as absurd as this you can write it off to say maybe she took self defense classes in her spare time, and she was just too insecure/scared to use them. The cat like traits like drinking milk is just her mind snapping and her acting crazy. Those kinds of things, even the three bad falls she had and survived unharmed, I can overlook all of them because although it's really unlikely there is a chance she could have survived them without any serious injury. I mean Jackie Chan has walked away from some really bad stunts gone wrong in his movies.
But the four gun shots at close range, there is no way any normal person is walking away from that without being physically debilitated in some big way. Batman Returns is not set in a world where regular people are immune to gun shots like that. Unless of course they are supernatural as the movie constantly has her say, and imply with all her miraculous survivals.