The Joker didn't have a single physical altercation with Batman. Ra's al Ghul did, but only as Ducard, while training the guy (subsequent to which Bale takes a few levels in badass, as the saying goes). Two-Face and Scarecrow didn't get much chance to mess him up either. They set them up as credible threats by doing things other than just screwing over Batman - Joker's breathless and sadistically murderous bank robbery set the tone for the character in a way that doing a number on Wayne never would have.
Granted, aside from maybe Ra's they were never depicted as people who could go physically toe to toe with the Bats, while Catwoman is. Even still, the sort of storytelling where two superheroes duke it out and they're both alive at the end of the fight, letting the defeated one slink away, is something that the Nolan films have mostly eschewed. One could easily show Catwoman's strength by having her thwack someone else - whoever the other major villain is in the film, say, as these pictures tend to have more than one. Or a whole group of goons. Et cetera.
Yeah, I tried reading up on the character on Wikipedia to make sense of her, and every paragraph just made my eyes glaze over. Alright, she's the Earth Two future past Supergirl when she isn't the Atlantean princess or yadda yadda gumdrops. I'll wait for the movie.
Hm. That's meant to be a punchline, but honestly, if it weren't for Hollywood's current reluctance to do female hero films I'd expect a movie with all those comic book properties getting churned out. They're even doing a comic book take on Thor, which is just so mind-boggingly weird to me. Can't I get a film about the mythic hero instead, please? But whatever, that'll be a weird sell outside of America, presumably.
Battlestar Galactica also had scenes during Gaeta's insurrection of Adama and Tigh hefting guns and kicking ass. If you're a main character and you're badass, logic frequently need not apply.
You've discovered the comedic nature of Power Girl's background. It's been retconned so many times I don't think anyone has it entirely straight anymore. The long and short of it is that I don't have any problem watching her smack a similarly empowered male villain around with a car. Realism is removed from the question when the hero is an alien from an alternate universe.
