One of the elite martial artists in the DC universe, Lady Shiva trained Batman, the current Robin, and Black Canary, and she's fought alongside the good guys on a number of occasions. But she's also a professional assassin, and thinks nothing of killing people, which doesn't exactly work for Batman.
Pros: Cool martial arts action, and an opportunity to explore some of Bruce Wayne's training to be Batman before the League of Shadows in Batman Begins.
Cons: A big chunk of Lady Shiva's story as it relates to Gotham comes from characters like Black Canary and Cassandra Cain, who don't exist in the films.
How I'd do it: Start with a flashback to Bruce Wayne after the death of Joe Chill but before the prison where Henri Ducard recruited him for the League of Shadows (he didn't learn to fight six (or seven) guys at once from some self defense class at the Gotham YMCA, right?), and he trains with Shiva. She's trying to teach him killing blows, but he refuses. Normally she'd refuse to train someone like that, but his passion to learn wins her over. Then we cut to the present day, and she's been hired by associates of Lau (the money launderer from The Dark Knight) to take out Batman. Lots of fighting, she probably figures out who he is, and... well Batman wins in the end.
Casting Guesses: I'm not really a martial arts movie fan, so someone will have to help me out here. An actress who can kick ass, look great, play both a 25 year old training Bruce and a 35 year old fighting Batman, and maybe speak English? Though it could work with subtitles too.
Verdict: She could really work. Fits in the world they've created, fills in some backstory that has to exist, nothing to goofy about the character. The role has to be cast well, which is obviously something I'm failing at, but with the right actress Lady Shiva could work well.
After The Scarecrow, Ra's Al Ghul, The Joker, and Two-Face, who should be Batman's next enemy in the Batman Begins/The Dark Knight series? Well, as of now we know that Tom Hardy will play Bane and Anne Hathaway will play Catwoman.
Check out the master list for all the villains covered. I've pretty much run out by now. Obviously, there are more Batman villains, but not any of significance that I know of. As of February 2009, no one is confirmed as a villain. Not the Johnny Depp Riddler, not Phillip Seymour Hoffman Penguin, nobody.