Wanted to give you guys everything I know about this (which is mostly obvious if you've tried it).
NOTE: If you die and the game starts you back at the beginning, quit out and delete that save file before re attempting this. If a death registers on an attempt that save file will never be able to unlock the achievement so it is important to start a new save file before continuing.
1. Yes, you can save your game, so it doesn't have to be done in one sitting.
2. You cannot make a backup of your save like the other modes. If you try, it just moves it.
3. You dont have to be online when you finish the game. This is hit or miss though. If you finish the game offline and this doesn't unlock when you reconnect, try closing the game and deleting the reserved space. Don't delete your player data, just the reserved space. Then relaunch the game while connected to live and see if that pops it. If not, you may have to re-do it, or at least re-complete the final escape while online.
4. If you're struggling, play offline until you've made 10-15 minutes of progress. Reconnect to live, save your game, then close the game and re-launch it. Load your game and save once more (to ensure your save syncs with live). Go offline again and try to make some more progress. If you die while offline, just delete your local save file (and the 1gb of reserved space, just in case). Reconnect to live and launch the game to re-sync with the older save file on live, then go offline to try again. I have confirmed that this method works.
5. If you happen to die while connected to live, pause IMMEDIATELY when you die, before the game over/retry screen comes up. Dashboard and delete your save data and the reserved space. Launch the game and re-sync with live, and if you're lucky you'll have the last synced data instead of starting over. See Razorpriest's comments below for confirmation that this *can* work.
6. Try to do this legit, even if you cheese it for the achievement. There is nothing more satisfying than completing this game on One Life mode without dying, without using any crutches.
Successful run starts at 1:34:30.
And just for extra reference material, a 100% completion speedrun on One Life.