Dungeons, dungeons and more dungeons. Especially anything where almost the entire dungeon is a specific dull colour, such as grey (I'm lookin' at you, cave dungeons) or brick (I'm lookin' at you, dungeon dungeons).

Snow areas tend to almost always be crap, too.

Still, for the sake of specifics...

I - The part where you want to put some personality into your characters, but nope.
II - The part where you have to grind because you realise you played the system all wrong.
VI - The part where you have to go up a tower without magic.
VII - The part where you have to constantly stop to warm up Cloud while going up a mountain.
VIII - The part where you don't have access to any towns, just because.
IX - The part where you start playing Chocobo Hot & Cold.
X - The part with Tidus, the part with Yuna and the part with Seymour.
XI - The part when you realise that each level is genuinely going to take that much longer. And there is nobody.
XII - The part when you stop doing hunts and collecting bestiary information and get back to the story and then realise that you don't know what the smurf is going on anymore.
XIII - The part when you get sent to that arc thing.
XIV - The part when content gets gated.

I haven't finished III and IV, and I can't remember anything annoying about V.