If you don't know Polish, the narrative gets in the way, but you can watch Bats skulk around Arkham's grounds and get a feel for the stealth takedowns the game is engineered to deliver.
I was particularly impressed by his ziplining up to a guard tower and clonking a sniper, forehead-first, into the railing. Of course, it required the guy to be completely oblivious to a 200-pound man grappling to the floor he was standing on, but hey. It's Batman. Also, what's up with the x-ray vision mode?
Later, Batman lays out some pretty gruesome hand-to-hand combos - you can see the finisher coming up when the camera speed slows down. The combos deliver you bonuses for varying your moves, so, button-mashers be warned.
Finally, this may be in Polish, but everyone can get that load-time joke at 5:40 right? Right? Otherwise, that's one hell of a cameo for this game.
Batman Arkham Asylum Gameplay Beta [YouTube, thanks excaliburps]