If you are having trouble getting it working:
1. Download the Batman_Arkham_City_TB_EBOOT_PATCH-PS3 rar
2. copy the original BLUS30538 to your External
3. Put the Backup files on the same drive in a different area or another thumb drive.
4. Copy the patched files in the multiman file manager to the BLUS30538 on the external
5. IMPORTANT: press  *square in gamelist area of multiman while Batman Arkham City is highlighted and dot the External radio button.
I was having all sorts of problems, but this combination worked for me, if you have already messed around with copying files from here to there just remove all the Batman Arkham City files of your PS3 and External and start from scratch Including the Trophy folder (NPWR01235_00). If the trophy folder isn't in your home directory, that's fine.
One last tip; copy all the language files too. I know you can get away with not copying them over with some games but that could have been the problem if you were one of the people that just copied the English files over.
Hope this helps.
I've been handed PES 2012 TB EBOOT, SPRX & PARAM. What to do, what to do? (I wonder if ANONYMOUS can do his magic with them?)