Without playing Arkham Asylum. I know both games are cheap at this point, it's more about the time commitment. --- "I wanted to buy a candle holder but the store didn't have one, so I bought a cake." -Mitch Hedberg - GT Skillz MC
Absolutely. There is some small stuff from the previous game that are referenced, but those are just minor things that add flavor for people that followed the stories closely. The story in Arkham City is self contained, and you'll have no problem understanding or following the story if you jump right into AC.