As a note, she had a major controversy regarding sexism. Comics have a bad history of killing off and maiming female characters (like Batgirl being shot and paralzed from the waist down, Supergirl being killed off at one point, Black Canary being brutally tortured and losing her canary cry, etc) at a high rate compared to male characters. When male characters are maimed, it's often for their own development (like Batman and his infamously broken back from Bane), whereas female characters have often been killed off or permanently power-stripped for decades for the development of a male character (Batman, Superman, and Green Arrow respectively for those three).
Stephanie Brown ran into the same problem at some point. After being robin for a while, fans liked her, but she ended up being tortured to death. And, her torture had some fairly sexualized imagery to it, which was pretty screwed up. And then unlike previous dead robin Jason Todd, she never got a robin memorial in the Batcave. Fans got pretty angry at that whole series of events.
Years later, Stephanie Brown was brought back, and she became...
Batgirl.
There was another awesome Batgirl named Cassandra Cain, who was basically the best martial artist in the DC universe. Historically Shiva has been the best martial artist, with others like Richard Dragon (he's probably tied with her), Bruce Wayne, Black Canary and others all being roughly top tier too. But Cassandra Cain kind of took that mantle when she beat Shiva in a fight.
Cassandra's character was neat because she was basically an odd prodigy. She was a Tibetan raised by the League of Assassins to be the perfect killer, and instead of being taught how to talk as a kid, she was taught martial arts. Like, she literally never learned how to speak, and was mute and antisocial. Instead, she learned from infancy to read people's movements, and had a prodigy ability to read people's movements literally as easy as a normal person can listen to speech, because that's the first thing she ever learned. She was also abused to be highly resistant to pain, and as Batgirl could take a bullet without showing much pain. She had her first assassination as a kid, but was so horrified by the ethics of it that she ran away, wandered the world for a decade or so, and then joined Batman as the next Batgirl. So basically in a fight, she was ridiculous, and not second to Batman in that regard (he still had his genius and tech and money, but he wouldn't do well to, say, fight her in a fair martial arts match, because she'd be one of the few normal humans to be able to beat him, even as a teenager).
Another female robin in one arc was Carrie Kelley, who had a very androgynous appearance which was neat.