Sharp took credit for getting the Joker situation of the first game under control. He then used that incident to help win the Mayoral election. After winning, he declares Blackgate and Arkham unfit, and buys off a portion of the slums of Gotham. Walling off the area and calling it "Arkham City", he contracts a mercenary group called Tyger into defending the walls. The prisoners are only given one rule: "Don't try to escape", with the penalty for doing so being death. Beyond that, they can do whatever they want within.
-Hugo Strange heads the new Arkham, though it seems like this fact is cloaked in mystery to the outside world. Those who look into him disappear.
-It's been a year. Two face is admitted into Arkham City and he realizes he has to make a move to assert himself in the new prison lest he be eaten alive (not literally, of course). He captures Catwoman, figuring a public execution should do the trick.
-The team is aiming for a highly detailed city, on the level of what they did in the first game with Arkham itself.
-Gadgets can now be used during fights- the article mentions Batman putting explosive gel on the back of one of his opponents during a brawl.
-You can now pull off multiple counterattacks at the same time.
-Many of the super villains have formed gangs, and taken control of differnt portions of the city.
-The team wants to push the "forensics" angle of the first game more, incorporating puzzles in them that will become more complex as the game goes on.
-Most of the key gadgets that were unlocked late in the first game are available by default (Beyond the explosive gel, the article also mentions the line launcher).
-Interrogations replace the Riddler maps of the first game.
-Batman can now taunt his enemies via a button press.
-Certain characters have optional sidestories within Arkham city (the article mentions Zsasz), that you can dig into.
-Harley has a new costume. From the article: "Instead of a nurse outfit, Harley now wears red and black pants, and a matching midriff-baring top. Her face paint has been scaled back to a much more subtle degree, and she now has a Joker tatoo on one of her hips peeking out over her waistband."
-Batman's been given a new gadget called the "broadcast analyzer". The article mentions several broadcasts Bats can listen in on, like the GCPD dispatch and Gotham FM. The main usage here has Batman tuning in to listen to a message left for him by the Joker.
-Oracle is missing, so Alfred is the one in Bruce's ear (at least at the beginning of the game).
-Rocksteady wouldn't detail their multiplayer plans.
