"We're all mad here" might be the best description of almost all of the characters in Batman: The Animated Series, including the caped crusader himself. Most of the villains in Batman are super criminals with personal obsessions that drive their crime sprees well beyond the point of parody. Of course someone named E. Nygma is going to be puzzle-obsessed and (when double-crossed in business) take up the mantle of The Riddler to gain revenge. Of course someone named Victor Fries is going to invent a freeze ray and take up the mantle of Mr. Freeze in order to get revenge on the man who almost killed his terminally ill wife. Of course Bruce Wayne dresses up in a mask and a cape and clears Gotham's streets of super villains. And of course the villains mostly end up in Arkham Asylum instead of Gotham Penitentiary. They're all crazy! Mad as hatters! (And yes, there is a Mad Hatter, obsessed with Alice. He vows revenge when Alice spurns his advances.)
What's different about the Crazy Ladies of Batman is how their motivations and actions are a bit...differentthan that of the various male characters. To steal from Nostalgia Chick's list of the top 11 Villainesses, these ladies aren't motivated by the death of loved ones, personal betrayal in business, or even romantic obsession. No no, these ladies are liberals gone mad.
The first of these women to be introduced is Pamela Isley. Seeing that the newly-planned Gotham Penitentiary is about to destroy the last remaining wild, thorny roses in the world, Isley vows revenge against Harvey Dent, the District Attorney who had the penitentiary built. And how does she get this revenge? By waiting patiently for five years, then seducing him into falling in love with her. Then, in true femme-fatale fashion, Isley kisses her fiancé with lips coated with poison that has been derived from the now completely extinct (except for one!) wild thorny rose. Batman discovers that his best friend's new fiancé is actually Poison Ivy, and they battle it out in a huge greenhouse filled with giant, man-eating plants. "The blood of those flowers are on his hands!" Ivy shrieks as they fight.
Our last glimpse of Ivy in her introductory episode is of her in the deep basement of Gotham Penitentiary rocking back and forth, muttering "They can bury me in the ground as deep as they like, but I'll grow back. We always grow back, don't we baby?" to her beloved thorny rose. (In later episodes, Ivy's kept at Arkham Asylum with all the other Crazy Villains.)
Our second Crazy Lady is animal rights activist and cat lady Selina Kyle. In the animated series, we first see her in her Catwoman guise, stealing shiny, shiny jewels in order to fund her animal rights activities. There's an obvious and instant flirtatious attraction between Catwoman and Batman, which allows her (at least initially) to distract him and get away. Later, Bruce Wayne meets Selina Kyle at a charity event (to support a wildlife reserve—Bruce is all into the social causes) and is instantly smitten, while Selina is cool and distant. Her real interest isn't in boring old Bruce, but fascinating and mysterious Batman. However, she's happy to use Bruce's interest to help her fight for a preserve for big cats outside of Gotham's city limits. Unfortunately, since the land the preserve would be on is wanted by the world's greatest terrorist Red Claw, Bruce's legal attempts to help her don't amount to much. Lucky she's a cat burglar by night so she can find out what's really going on!
Catwoman's motivations are a bit more complicated than Poison Ivy's. She spends some time trying not to be a villain, but then slips back into her villainous ways. She occasionally helps the Batfolks (Batman, Batgirl, and Robin) out when needed, but obviously enjoys being a cat burglar. I don't think she ever ends up in the Asylum like the other villains of the show, but she certainly has an "obsession" with all things catlike. Also, of course, she's a femme-fatale, one of Batman's weaknesses. "Never trifle with the affections of a woman," she shouts after tossing him off a very tall building.
Our final main Crazy Lady is the infamous Harley Quinn. She's introduced as The Joker's sycophantic fangirl in Joker's Favour, eager to do her beloved Mr. J's every whim. But Harley's true delve into Crazy Lady territory comes from her backstory. Harleen Quinzel used to be a psychiatrist, one who was determined to really understand the true motivations of someone like The Joker. She believed everything he said about having a terrible childhood that led to him being such a violent criminal (like a true bleeding-heart liberal!), and fell in love. Obviously, her only answer to win The Joker's affections was to turn to a life of crime herself. Throughout the show, her love for The Joker, and his answering violence and taunting, is a pretty terrible story of an abusive relationship where Harley believes that her "Puddin'" really does love her under all that violence and misunderstanding. She ultimately ends up trying to kill Batman in order to get rid of her only competition for The Joker's affections.
Harley is allegedly quirky rather than anything else, although it turns out she's as murderous as the rest, willing to do anything for the affection and attention of The Joker. While she occasionally goes on crime sprees with Poison Ivy, she really doesn't seem to have any of her own drive to commit crimes. She's just in love. A true femme-fatale.
And that's what I find most interesting about our crop of Crazy Ladies in B:TAS. Each one of them is introduced as a love interest. Each one uses their appearance to manipulate men, be it by wearing sexy costumes or by appearing as non-threatening as possible. Each one's motivations aren't really personal betrayal, à la Nygma, Freis, or the Mad Hatter. They aren't Just Plain Crazy like The Joker. They've got these huge motivations, are often presented at least somewhat sympathetically, and are all femme-fatales.
B:TAS is in the style of film-noir, where all the women are beautiful and all of them use their beauty to gain something. It's a show in which freeze rays work and there's a big green pit that you can bathe in and recover from death. But at the same time we see a lot of recurring tropes we've discussed earlier in the series. As Crazy Ladies, their motivations are over the top. Therapy is ineffective or just a smoke-screen. Arkham Asylum is a pretty standard pop culture mad house. And, much like the women in the asylum of Sucker Punch, sexy costumes for everyone.
It's almost like the same tropes show up every time Crazy People get a story in pop culture, isn't it?