I had a lot of fear going for this achievement and it seems like there was still a lot of confusion and conflicting statements on this one adding to my fears that I screwed it up. Even after reading hundreds of posts I wasn't sure if I was screwed or not but here's exactly How my unlocking this achievement played out if it alleviates any other gamers fears great! For starters I went for this legit.
I played offline. Did not have patch/update installed. Played all the way to end of Arcadia level without reading that there were issues with achievement. Died roughly 5-10 times between start and Arcadia (esp. facing first two BDs). Once I appears in VITA I never hit the "A" button to respawn. I always immediately loaded up a save file. Then I installed the update and played all the way to Olympus without dying at all. Then I reinstalled the DLC because I had the glitch where it wouldn't let me turn off VITAS. Now I disabled VITAS at Olympus. Played to the end. Achievement POPPED. Many gamers said they loaded save and killed Atlas and it popped and they prolly didn't have the update until they did this since they came out at same time. Gamers have said that they died but loaded saves and it didn't pop for them so my opinion is either
a) the update/patch starts logging/tracking whether you die and appear in a VITA or
b) physically pressing the "A" button once in the VITA and then attempting to load a save
is what's screwing ya. 5 years in the making and this game is finally DONE! Whoo!