All the way 5 stars.
Batman Arkham Asylum is a surprisingly good game. After having played the Demo i thought, "...s'alright", but after having played the game i can tell you that it stands out as one of the best games of the year.
What the demo doesn't show you is the "Metroidvania" style gameplay where you have to upgrade your equipment to get to the next area. The game is made of many parts; exploration, platforming, stealth and combat.The combat is saticfying enough, though the weakest part of the game. You can get through the game well enough by button mashing these combat sequences but if you try to be more precise in your timing you'll find that you can string together better combos. Stealth consists of mostly hiding from armed thugs on gargoyles to avoid being seen as you take them out one by one. Though it may be too easy to "lose" your victims the process is a very satisfying one and utilizes your bag of bat tricks. Platforming and exploration...it's there. You may not expect it as the game comes across as an action combat romp.
All these parts make for a very satisfying game all around and definitely should be checked out. Even if you've been burned before Batman AA stands tall on it's own with or without the license...It's a flat out good game.