Batgirl vs. Joker

Nope, not Barbara Gordon but Cassandra Cain. See one of the problems Cass faced, as far as writers were concerned, was how to avoid making her too good. Yes she would later become the best fighter in the world when she defeated Shiva (which somehow lead to her turn to a villain) but long before that there were concerns. This may be part of the reason for DC being reluctant to use her character or at least part of the reason. Of course it's debatable if DC is making that mistake with Damian but that's a story for another day.

 Her skills have been hard for some to understand as the writer infamous for her fall from grace, Adam Beechen, thought Cassandra fought others by reading their fighting style. That's not how it works. She reads one's body movement to determine their next move, their emotions, even if their lying. Cass ran into trouble with those who's actions were hard to read like Deathstroke (who was always thinking five steps ahead), Rose Wilson (who's a precon) and the Joker. Now most would assume the Joker would be easy for a great fighter like Cass. If I remember correctly most of the bats thought that as well. Only he was hard to read much less understand. Cass was overwhelmed by confusion and got hurt because of it. Interesting stuff showing that he can be threatening to every member of the family.