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

Go to the directory of game, \Batman Arkham City\Binaries\Win32.

Right-click on BATMANAC and go to Properties. Click on the Compatibility tab and check Run this program as an administrator. Then, delete xlive.dll from the folder.

Now, go to C:\Program Files\Microsoft Games for Windows - LIVE\Client or the appropriate path for your computer, and right click on GFWLIVE. Make sure that program runs as an administrator as well.

Finally, start Batman and press the Home button.