AA does some things very well. The stealth and detective mode really add to Batman's character and make it more than a next-gen side scrolling brawler. Kudos for realizing Batman is about more than kung fu-ing generic thugs.
The sore point of the game, IMO is the combat, which is a shame because it is such a large part of the game. When you go up against small groups of 4-5 thugs, everything is fine. When you take on any more than that, the camera works against you because enemies will circle behind you, outside of camera view, and attack. Not being able to see them means you suffer cheap hits, break your combo, and take heavy damage. The damage seemed pretty severe to me, with a single hand to hand blow taking off a large chunk even if you upgraded to the lvl 4 armor. Weird.
The "bosses" are weak too. Zsaz is nothing more than a generic knife thug you see throughout the game. Bane is cool when you first face him, but soon you see he is exactly the same as the Venom mutants, many of which you have to fight two of at the same time along with some thugs. The last battle with Joker is a joke, especially when you consider how difficult the fight right before it was. The Scarecrow bits are really cool, but he isn't what you would consider a traditional boss. IMO, the only one that stands out is Ivy. She is a unique encounter unlike any other in the game and has a discernable pattern you need to exploit to defeat her.
I'd say the game gets a solid B, but I think some of the mid to high 90s scores it has been getting are vastly overrated.