No, she isn't supernatural, doesn't actually die, doesn't become half cat and doesn't really have 9 lives.
Well, I must be mistaken because the version I saw, she fell to her death. Cats brought her back to life. Throughout the film she got shot, choked and fell from great heights but survived. So all these things were luck escapes and coincidences? The intention of Burton was pretty obvious. She was a normal woman who, after a supernatural event, became Catwoman. It was never explicit but was certainly there.
Warner Brothers wanted Penguin because they thought he was the next top villain on the list, and Burton wanted Catwoman because she is his second favorite Batman villain, so they compromised and included both and Burton came up with his own interpretation of the Penguin because the Penguin in the comics back then was just a silly little fat man in a tuxedo with a rainbow colored umbrella who committed bird themed crimes. Burton made him far more complex and interesting then he ever was in the comics.
I don't really care for the Penguin as a character. I find it kind of forced that a guy who is born with a Penguin deformation just happens to be raised by Penguins as well.
Burton certainly does get Batman. Burton understands that Batman is a serious, dark and mysterious character and captured that very well.
He certainly understands those aspects. But Batman is more than a serious, dark man of mystery. He's determined. He won't sit around waiting for the bat signal every night. He will be out fighting crime regardless. He won't sit back and kill people in his Batmobile, burning them alive or gunning them down with machine guns. See any of TAS, BB or TDK for a closer interpretation.
I don't mind BR for what it is. It is much better than BF and B & R. It's a decent Burton film. But after seeing countless Burton films with the twisted fairytale theme and Danny Elfman music, I see BR as just another of the films he wants to make. He didn't set out to make a faithful adaptation of the comics. This is a movie he wanted to make with Batman inserted as the main hero.
What I like about BR, and always did, was the idea of having a Bat, Cat, and Penguin as the main villains. What a great marketing idea. A great idea for story themes as well. Then Burton made it about damaged orphans. Another smart move! Then...Penguin runs for Mayor. Ok...Then the bad guys frame Batman...no, that's crap.
That's the problem. The whole film has great themes but a lousy story and mostly lackluster action too. I find it catastrophic that Gotham would think Batman would just randomly kidnap and murder someone. The guy who always saves the day and vanishes, all of a sudden kills an innocent person and leaves the murder weapon. How will Gordon solve this shocking crime?! AWFUL. No matter how much of a following BR has, there is not one person who could tell me this is a great idea for a story.
Penguin as mob boss. A great idea? Political satire? Perhaps the Penguin represents every candidate, preened into power? Perhaps. But I think, again, the writing has let a potentially wonderful idea down. I don't buy that the people of Gotham would suddenly love this disgusting monster from the sewers. Is this the same place from B89? Nope. It feels like some weird Burton film...because IT IS.
Burton makes these kinds of films. Weird, twisted fairytales with supernatural themes. That's his thing. He made BR one of his many twisted films and made it somewhat interesting but it is not a Batman story.