In a nutshell: Which is your favorite Batman: Arkham game? Most people will pick either the original (Asylum) or its 2011 sequel, Arkham City. Warner Bros. never reveled how many copies the latter sold, but thanks to a company exec's LinkedIn profile, now we know: a lot.
The figures were discovered by Twitter user Timur222 (via PC Gamer), who found the figures on the LinkedIn profile of a former global franchise marketing manager that worked for publisher Warner Bros. at the time of Arkham City's release.
The profile mentions Arkham City explicitly, with the ex-employee stating they "strategically marketed a AAA life-cycle campaign to deliver over 12.5m units (2011 – 2012)." It also mentions that the game raised $600 million across the many platforms where it's available, and the person "managed co-marketing partnership valued $5 million."
Gamespot writes that Arkham City shipped 6 million units in the four months following its release in October 2011. Having reached 12.5+ million in its first year is very impressive, and we can only hazard a guess at how many units the game's sold to date.
Arkham City remains the best-reviewed entry in the franchise. Its average of 92 puts it above Asylum (90), Knight (83), and Origins (74). Although those who remember Arkham Knight's disastrous PC port, which resulted in sales on the platform being suspended, may place it last.
Being such a money-making franchise means we'll almost certainly see another Arkham game, possibly this year, though it's unclear how the potential sale of Warner Bros. Interactive by AT&T might affect development.