Just going to repost this form the PC version thread, as a warning:
So I finally got home to try what I was thinking, and here is what I can confirm because of it:
1) Steam versions of the game save only to this directory:
Steam > userdata > 38578650 > 57400 > remote and are formatted like this
username-save#.sgd (with the # being the slot of your safe, the first slot is "0" and the 4th sloth is "3").
2) Presumably, other versions of the game save to this folder:
Documents > WB Games > Batman Arkham City > SaveData. If you have the Steam version, this folder will still be created, but it will be empty.
If you are hit with the "we deleted your save because fuck you" bug, take these immediate actions:
1) Do not click through to the save to see if it is actually deleted. If nothing is there, it is gone.
2) Alt-tab out immediately and navigate to the directory where you save file should be. Copy it out if it is there. If it is already gone, then, I don't know. They've wined and dined you and now you're screwed.
3) Close the game down and start it back up, if it still is showing no save, close it down again, and copy your save file back into the directory.
4) Load up the game again and hopefully you should have your save file again.
This should work, but I was only able to confirm it using newly created save data. (I played to the point where I made some progress, just after you
and tested my theory with swapping save files)
What you should do right now, even if you are a big-shot who lives by his own rules and on a razor's edge: go to your save directory and make a personal backup of the save right now. Don't let what happened to me happen to you, where I lost 24 hours of progress because it randomly deleted my save then synced that it to Steam cloud. There is no way for me to recover my save data now.