Beat The Game, Try It Again!
Rocksteady have long denied the existence of a 'New Game +' in Batman: Arkham City. It's a great feature sorely missing from the original, but it appears Rocksteady have wised up and changed their minds for the sequel, as New Game + is indeed in Arkham City, activated upon completing the main game on Normal or Hard difficulties.
So, you've completed the game on Normal or Hard - well done - and you want to run through Arkham City again. New Game + will appear as a difficulty setting - and, yes, you can play the game again without it activated. New Game + grants you all the experience and gadgets you earned in Arkham City, but counters your superior arsenal by removing counter icons from combat, increasing the toughness and variation of thugs and henchmen and transforming boss-battles from difficult endeavors to lost causes.
This is sure to delight fans you were crying out for the mode in Arkham Asylum. Rocksteady have not commented over whether Achievement and Trophy progress will still be recorded while New Game + is active, although I sort of doubt it. [Rocksteady Forums]