Done this in the FFIV forum already: which version did you complete first, not just play? Cheating or hacking doesn't count either!
I first beat the PSX version, then GBA, then NES, which I'd previously attempted several times but never done despite always making good progress... then one day I stopped using Black Mages and the game always beat itself after that. I'm a bit of a loser I'm afraid. Ironically the PSX version I've only beaten once in contrast to those other two which I've aced dozens of times each.