The optional bosses were easily the hardest part in the game, good thing they were optional.

If we're sticking with mandatory moments, though... I found the fighting Jenova, and Sephiroth three different times to be the hardest part, especially when you got a game over mid-way through. Once I got some grinding done, though, that part became easy. I was always crap at the Golden Saucer and getting those treasure chests on the train track.