Alright, running the Batman: Arkham Asylum GOTY in-game benchmarks. V-Sync Off.
Multi-Samping Anti-Aliasing (MSAA): Off
Resolution: 1920x1080 (16:9)
Setting at Very High
Min FPS: 76
Max FPS: 204
Average FPS: 155
Multi-Samping Anti-Aliasing (MSAA): On at highest (x8)
Min FPS: 75
Max FPS: 178
Average FPS: 134
Yep, this card can run the game pretty well. Note, that I have an MSI R6870 Hawk 1GB. It's factory overclocked, I didn't do clock it any higher than the manufacturer. A great card for me
You may want to turn your V-Sync on, because there will be screen tear, there is so much frames this card has, the monitor will go out of sync lol.