DX11 in Arkham City was a performance-killer, especially when mixed with PhysX. If you have both of those enabled, even with a high-end card like the 670, it might just be the game.
I have a vanilla 660, so a card that's a bit slower than yours granted, but at 1080p I still can't play Arkham City with both PhysX and DX11 turned on and get console-level framerates. Turn off DX11 and I can't tell a difference in quality but the framerate spikes up and holds steady at what I beleive to be roughly 60fps at all times.
I do not understand what I do. For what I want to do, I do not do. But what I hate, I do.