This is undoubtedly the best comic-book-hero-based videogame ever made
The story is as well written and voiced as of the recent Batman / Superman / Justice League cartoons of the past decade, and while there is a linearity to the story line (because there has to be, duh) you are free to use your own means in finding ways to defeat groups of foes. If you want to jump in a rumble mano-a-mano, go for it. If you want to creep through the shadows and take each thug out one at a time, you can do that too. I actually lured a bunch of guys into a trap and took them all out at once, and then giggled like a schoolgirl that the game allowed me that much freedom.
Atmospherically, this game makes you wonder why any sane person would ever go to Arkham Asylum--patient, doctor, guard--who would want to be caught in this desolate place? It makes Batman all the more remarkable not only for his willingness to go to this place, but his ability to contain it.
I could go on and on, but I would simply say that if you're a fan of comic book heroes (especially Batman) or third-person action adventures, then you really need to give this one a look. I can't recommend it highly enough.