Recover save games in Far cry 3

The game does not give you the direct oppurtunity to have multiple save files for one playthrough, so you will have to go to the "system settings" -> "memory units" -> "memory device holding your saves" on your xbox and then copy the savegame you want onto a different device (e.g. USB stick).
That way you have a backup if the savegame corrupts.
It is a lot of effort but the only way to do it without a modded xbox, sorry.

There are 3 missable things: The achievements "Unheard" and "Fully Inked", and the alternative ending. Everything else can be done after you played the story to its end, as you will still be on the islands.

Try disabling crossfire. Many games do not play nice with multi GPU setups. I have a 2GB 6950 and the game runs fine for me.