Oh boy, I've been meaning to write about this game for ages. By which I mean, when it came out. Let's get this out of the way then, shall we?
Batman: Arkham Asylum is obviously a license game, and license games tend to have a certain kind of... reputation. Worry not, Batman is actually a good license game. Well, mostly, but we'll get to that later.
So, the story of the game is fairly basic - Joker gets locked in AA, but it was actually his plan all along and chaos ensues. The story is fairly basic, but it works well enough to maintain interest in the game and getting the player to move through the game. Along the way Batman meets some of the more iconic villains of his history - Poison Ivy, Bane, Killer Croc and so forth. Of course, since the game is about Batman, we also have all kinds of gadgets to use, including Batarangs and gliding with the cape.
Most of the gameplay consists of Batman doing sneaky things and moving in the shadows, sneaking and lurking around, constructing plans as to how to take out the many minions and henchmen of Joker. And this is where the game excels, the sneaking is masterfully done and feels just right, and when it comes to fighting hand to hand, the game really shines. The combat is fluid and building combos feels incredibly tight. This is one of the best combat systems in any beat 'em up-games ever, if I may say. The combat is spiced up by different kinds of henchmen - some have no weapons, some have pipes or electric batons and some have firearms, and firearms are something to be wary of. Luckily Batman has "detective mode", through which he can easily find the armed henchmen and find ways to disable them.
So, the combat system is great. How about boss fights? Sporting quite legendary names in the villain repertuary doesn't unfortunately mean the boss fights are good. They are easily the weakest part of the game. Only two boss fights are something I'd say to be actually good, and those would be Scarecrow and Killer Croc, and Croc isn't all that good. Bane-fight is ridiculously stupid and simple, and Poison Ivy is your run-from-the-mill boss fight where you have to hit her thrice in certain spots (don't understand it like that, perv!). But Scarecrow is one of the most memorable parts of the game.
The game has great attention to detail. Many places have hidden Riddler-trophies, and finding all of them unlocks all kinds of cool stuff. Batman's cape gets more rugged as the day progresses on the Arkham Asylum, and so. Returning to old locations is often rewarded since you now have new gadgets giving you access to places you didn't have previously. The game has a good visual style and looks very nice.
All in all, if you happen to stumble upon this game for your platform of preference (PS3, X360, PC), I'd really suggest picking it up. It's one of the biggest games of this generation, and rightly so.