Batman Arkham City freezes when searching for Mr. Freeze
It might be worth seeing if you can activate your serial code (presuming you got one with the game) on Steam. The game utilises Steamworks on Steam, so there's a small chance that might work. Once that's done, just install it on Steam (and yes, Steam should ignore region locks if you have a valid product code, I think) and see if that works.
I have absolutely no idea if that'll work for you, as retail code activation doesn't always work for games that don't force you to use Steam anyway, but it's probably worth a shot..