Is there much to do after the Batman Arkham City story mode is finished?

I want to know that if you have finished Batman Arkham city , is there more stuff to do? For Example In Mw2 you can go online once your done with the story mode. In Arkham City do you do stuff like that?

Thanks.Is there much to do after the Batman Arkham City story mode is finished?
I have beaten Arkham City and once you have beaten it, you can go back, fight the criminals around the city, solving riddler puzzles, saving hostages, collecting riddler trophies, and completing side missions. If you want to get out of story mode, you can play challenge mode and complete those, the more trophies and puzzles you solve, the more challenges you unlock, plus if you want to spend the extra money, you can get the robin and nightwing dlc which gives you 4 unique maps and 4 skins. If you plan on buying it, don't worry, you'll spend a long time trying to complete the game 100%.Is there much to do after the Batman Arkham City story mode is finished?
I know you want an answer from someone who HAS the game and BEAT it, but I can tell you what I've read on forums of the game. After you beat the game, you can search for those riddler trophies, riddler challenges, and this time you can fight criminals (when in arkham asylum, there weren't any) as they can randomly spawn just about anywhere.