It was one of the best games of 2011, so it rightfully sold a heck of a lot.
During Time Warner's financial report for the year, they announced that the critically acclaimed Batman: Arkham City has shipped over 6 million units since its October launch.
For the company, Time Warner's Filmed Entertainment branch (which includes game development) enjoyed a 9% rise in revenue to $12.6 billion for the fiscal year ending December 31, 2011. They attributed this increase to a "stronger game release slate" and specifically cited Arkham City , Mortal Kombat , and various LEGO titles. We didn't get specific sales numbers for any title, but according to the NPD, the game was the 7th best selling title in the US in 2011.
We figure the game deserves it.
Related Game(s): Batman: Arkham City