Okay alignment is a can of worms. Here's my take:
Having a personal code and being Chaotic are not mutually exclusive. I've got this old Dragon with a 6-8 page article discussing 1E Barbarians (also chaotic) and their deep set codes of honor. The short of it is that Chaotics can be just as honor-bound as Lawfuls. Their honor is just a bit more personal.
I've also seen Chaotics to be _more_ inclined toward a code against killing. Each _individual_ matters to them more than to a Lawful (the big-picture folks), so they are more inclined to seek rehabilitation. Of course, Bats' reasons are more Lawful (loss of control, not descending to their level) than simple pacifism.
I guess I'd chalk him up to NG. I have a real hard time saying that someone who, by definition of being a vigilante, regularly goes around a basically Good police force is Lawful. At the same time, he has a fair bit of respect for the law and works with Gordon a fair bit.
He'd like to see the law work, really. He's just too pragmatic (and self-righteous) to believe that it will. So he does what he has to to get the job done.
In other words, if the "System" works, he'll use it. It ignoring, or even weakening the System works, he'll do that, too. He shows no allegience to either established order or to tearing it down. Almost a textbook definition of NG, so far as I can tell.