"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... different... than that of the various male characters. To steal from Nostalgia Chick'slist 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.
One trait I see portrayed frequently but not often discussed is mental illness and how it is used as a mechanism to propagate or explain away the actions of characters. Often, I see mental illness used as a tool to demonstrate just how terrible a character's actions are when their actions could be held up to scrutiny on their own. The use of mental illness as an agent of character development is an old trope that has been used time and again, often marring really great games. Outside of social justice circles, though, I don't see a lot of pushback against these depictions.
While the decision to paralyze Barbara Gordon was certainly a misogynistic one, the way that her character develops after the shooting speaks to the transformative power of information and technology...and librarians! Last week we looked at Barbara Gordon's character prior to The Killing Joke. She was a librarian by day and Batgirl by night. Her role as a librarian disguised her alter ego as Batgirl; reasserting the stereotype of librarians as meek and the opposite of badass. But this all changes after The Killing Joke. Thanks to a few writers who decided to make the best of what had happened to Gordon, Gordon's character decides to embrace her identity as a skilled librarian. She becomes Oracle, a computer hacker who discovers that access to information is a pretty phenomenal superpower.