This was copied from Arkham City.co.uk as it is a perfect summary of what we know so far about Batman Arkham City.
The Story so far.
Its one year after the events of Arkham Asylum and Quincy Sharp is taking full credit for controlling the “Joker incident” This has gotten him a lot of support from the city of Gotham and has resulted in him becoming Mayor. His first action is declaring that Arkham City and Black Gate Prison are unfit to hold inmates. He then proceeds to buy off a portion of the slums and names the area Arkham City. He walls of the entire City and contracts a mercenary group named Tyger to defend the perimeter of the City. Sharp announces that there is one rule and one rule only: “Don’t try and escape” the penalty for this action is death. This though is the only rule of the City. Prisoners are free to do what ever they wish and with Hugo Strange now in charge things get messy.
Two-Face gets put into Arkham City and realizes he needs to make a huge impact on the current inmates to prevent him from being eaten alive. He then captures Catwoman and proceeds to announce an execution; believing this will accomplish his goal of making him a powerful figure in the City.
The Gameplay so far.
All of Batman’s gadgets from Arkham Asylum return in the sequel, most of them are available from the start but it was never confirmed if all of them will. There is now a Broadcast analyzer featured in the game. Claimed to be mainly used to receive messages from joker; there are several broadcasts Batman can listen to including: GCPD Dispatch and Gotham FM. Oracle has gone missing, forcing Alfred to fill in as Batman’s aid. Combat has been tweaked to allow dual counters and easy access to gadgets. Rocksteady used an example of putting explosive gel on the back of enemies, along with this Batman has his smoke bomb back. If thats not enough to torment your enemies with you are now able to taunt them using an un specified button press. Rocksteady have claimed to want a very high detailed city and are hoping to use more of the “forensics” angle from the first title and incorporate puzzles in them that will get more complex as you progress. Gangs leaded by powerful “main villains” now roam the city, these are logged into Batman’s Criminal Database, Riddler's gang are able to be interrogated for the location of his hidden items. Side stories of featured characters are now playable, Zsasz’s is confirmed and finally, Rocksteady are currently not talking about any multiplayer plans yet.