too easy go to the directory of game \Batman Arkham City\Binaries\Win32
 right click on BATMANAC Click on compatibility tab check RUN THIS PROGRAM AS ADMIN.
 and delete xlive.dll from folder. now go to (or any other)C:\Program Files\Microsoft Games for Windows - LIVE\Client 
and right click on GFWLIVE and Click on compatibility tab check RUN THIS PROGRAM AS ADMIN.
NOW START BATMAN AND PRESS HOME BUTTON
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