Batman: Arkham Asylum Save Game Location

Windows

Batman: Arkham Asylum save games can be found on Windows here:

C:\Users\[user_name]\Documents\Square Enix\Batman Arkham Asylum GOTY\SaveData\

Steam:

Batman: Arkham Asylum save games installed through Steam can be found on Windows here:

C:\Program Files (x86)\Steam\userdata\[user_id]\35140\remote\

Linux

Batman: Arkham Asylum save games can be found on Linux (Proton) here:

~/.steam/steam/userdata/[user_id]/35140