Batman: Arkham City Save Game Location

Windows

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

C:\Users\[user_name]\Documents\WB Games\Batman Arkham City GOTY\SaveData\

Steam:

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

C:\Program Files (x86)\Steam\userdata\[user_id]\200260\

Linux

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

~/.steam/steam/userdata/[user_id]/200260