Oh yeah. That's right. I'm forgetting details of a game I haven't even finished yet. =S
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I don't think anyone has ever even seriously attempted that. As far as I know I'm the only person who attempted to put the No Sphere Grid and Initial Equipment/No Customization challenge together, and even just those two turn out to be impossible.
NCU (no crystarium challenge) has been completed in Japan, and it was recently completed with the english version as well.
Here's a link to the gameFAQ's thread and page at the point where the game was actually beaten without using the crystarium:
NCU United 3 - Final Fantasy XIII Message Board for PlayStation 3 - GameFAQs
And here's the youtube vid of him beating the final phase of the final boss:
YouTube - Final Fantasy XIII [ENG - No Crystarium Usage] Final Boss 3/3: Orphan 2
I think it's initial equipment part. I've never seen that be possible. But with that criteria absent I've seen damned near everything else mentioned and this looks a bit elaborate for a hoax! It basically relies on ridiculous item spamming.
You did make it pretty darn far though - beyond a part that was thought to be impossible. Almost to the very end of the game.
I have yet to even play FFXIII myself, but the Doom-thing (which, from what I've understood, results in a Game Over when the time runs out) sounds like biggest issue.
I suppose a FFXIII challenge would have to require a handicap that doesn't make your offensive capabilities suffer too much, in order to get past some of the Doom-bosses in time.
Edit:
Good news. (Though I won't watch the videos myself yet, as I haven't even played FFXIII normally). >_>