Green Man Gaming has Batman Arkham City: Game of the Year Edition on sale for $7.49 (75% off). You can then combine this with a coupon voucher for 20% off to bring the price down to just $6. Use the coupon voucher GMG20-PJFEW-Y16HK at checkout.
This is for the digital PC version of the game only. Batman Arkham City is a Steamworks game and requires the use of the Steam client in order to play.
The game of the year version of the game includes the base game as well as all DLC.
Make sure to check the system requirements before purchasing. This game has a large download of about 17 GB.