Just a Heads up for you guys, but I got this by utilising, or exploiting if you prefer that word, the cloud save system.
According to DarqStalker (and EricGarcia4) it's possible to save the game even further along than what I did.
DarqStalker
At the last cutscene, quit the game. This will save the game there.
Continue, watch cutscene, pick yes.
Once achievement pops, press guide button, and go to your saves to delete from console only.
Start up the game, continue, rewatch cutscene, select no.
Both endings complete!
I'll leave my steps as well:
Basically what I did was QUIT out Just after I did the final puzzle (I thought it would put me after the puzzle, but it didn't, it put me at the beginning of it) to force the game to save to the cloud.
Afterwards I started the game back up, did the final puzzle again, watched the cut scene and when I was at the Phone Section I choose to pick it up (I don't think it matters though).
When the achievement popped I ended up waiting until the achievement text had disappeared before I deleted my save.How to delete your save locally:Press the start button, hover over the game from the menu and choose Manage game & add-ons.
DON'T QUIT THE GAME or it may upload your save to the cloud.
Then go to saved data. Now Press
Delete from Console.
Don't delete it everywhere or you'll have to do the entire game again. You may have to delete it more than once for it to disappear.
Now load up the game and let it sync your save data and pick the opposite of what you did the first time around
From what I read online this is not a guaranteed way of getting it, but if you can get it to work you'll save yourself 30 minutes of suffering playing through the game again.
Good luck people!