Save Location
Retail
shell:personal\Eidos\Batman Arkham Asylum\SaveData
GOTY
shell:personal\Square Enix\Batman Arkham Asylum GOTY\SaveData
Steamworks
After the transfer to Steamworks save game locations changed and can be found at:
Steam\userdata\<userid>\35010\remote
Steam\userdata\<userid>\35140\remote
Transferring saved games from GFWL to Steamworks
A guide for transferring the saved games from the old GFWL to the new Steamworks framework can be found at http://steamcommunity.com/app/200260/discussions/0/810938810549705289/