This review does not contain any spoilers.
If you have played Arkham Asylum and enjoyed it, then this is definitely for you.
The game takes the story forward, though it is not a pre-requisite that you play the first part. The premise is grim, as in the Christopher Nolan films. Without giving the plot away, must say that I loved the story. I personally love a good narrative and this one didn't disappoint.
Its expansive with a lot of characters from the Batman universe, coming in at various points in the game.
For those who haven't played this series before, Arkham City is an "open world" set-up with a core plot and several side missions (which too were very nice). The visuals were fantastic and so was the voice acting.
Besides the awesome (and occasionally complex) fighting system, the game also has several puzzles which ensure your highest interest at all times.
The game also features a lot of extras including multiple costumes, maps, challenges etc. which will keep you hooked on for replay value.
Looking forward to playing more in the Arkham series.