Selina Kyle: Ok, Intimidate me, bully me if it makes you feel big. I mean it's not like you can just kill me...
Max Shreck: Actually, it's a lot like that.
Selina Kyle: Honey, I'm home. Oh, I forgot. I'm not married.
Selina Kyle: It's the so-called "normal" guys that always let you down. Sickos never scare me. At least they're committed.
Max Shreck: Bruce Wayne, why are you dressed as Batman?
Catwoman: Because he *is* Batman, you moron!
Max Shreck: Women. Nothing surprises me Chip, except your late mother. Who'da thought Selina had a brain to damage? Bottom line, she tries to blackmail me, I'll drop her out a higher window. Meantime, I got better fish to fry.
Selina Kyle: Mistletoe can be deadly if you eat it.
Bruce Wayne: But a kiss can be even deadlier...if you mean it.
[Bruce and Selina realize each other's identities.]
Selina Kyle: Oh my god. Does this mean we have to start fighting?
The Penguin: Don't adjust your sets. Welcome to the Oswald Cobblepot school of driving. Gentlemen, start your screaming.
The Penguin: Why does somebody always bring eggs and tomatoes to a speech?
Selina Kyle: It's gonna be a hot time in a cold town tonight.
Bruce Wayne: You've got sort of a dark side, don't you?
Selina Kyle: No darker than yours, Bruce.
The Penguin: They wouldn't put me on a pedestal, so I'm layin' them out on a slab!
Catwoman: I don't know about you, Miss Kitty, but I feel so much... Yummier.
The Penguin: Touring the riot scene. Gravely assessing the devastation. Upstanding mayor stuff.
Alfred: Why are you now determined to prove that this Penguin is not what he seems? Must you be the only lonely man-beast in town?
The Penguin: I could really get into this mayor stuff! It's not about power! It's about reaching out to people! Touching people! Groping people!
Penguin: Helpless old lady at twelve o'clock high!
Catwoman: You said you were going to scare the Ice Princess.
The Penguin: She looked pretty scared to me.
The Penguin: You've gotta admit, I've played this stinking city like a harp from hell.
Batman: What do you want?
The Penguin: Ah! The direct approach. I admire that in a man with a mask.
Answer: The film keeps it ambiguous. There are two ways to look at it. Scenario A- She literally died and is brought back to life by the alley-cats somehow, adapting some of their traits. Or... Scenario B- The trauma of falling and sustaining a head-injury, along with her paranoia after Schreck tried to kill her, has driven her mad, and she uses her connection with cats to build a new persona. (Which is supported by the fact that all the things she claims "kills" her with each of her "nine lives" wouldn't actually have killed her. Ex. Her one fall is broken by the kitty-litter truck. Max doesn't hit her in any vital organs when he shoots her. Etc.) Her destroying her apartment is her lashing out at all the things she used to hold dear- her vision of a normal life, etc. It's symbolic of her purging the past and embracing the future. (Plus, oftentimes when people throw fits, they'll smash stuff up).