These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Generally, monsters that can spam skills that damage your entire party, although thankfully they tend to use these in moderation. There can be up to nine monsters in a party and you can face up to three groups at a time. Needless to say, anyone with poor magic resistance falls quickly to such a barrage, unless protected from magic.
Anything with an AP drain poison. Some enemies can cast it on four targets at once. The only mercenary with the skill can (randomly) apply it to one target within the limitations of melee attacks.
Goddamned Bats: Anything with the Explode skill. Not only do they deal huge damage with it, they also die without leaving you a corpse to loot and won't count for quests if they die this way. Also, bats and other flying monsters cannot be targeted by normal melee attacks (or cannons), making them a pain for melee-heavy groups, and yes, there are exploding bats.
That One Attack: Mimics on the Ghost Ship have an attack that freezes your entire formation.And they start casting it on the third turn. And you can encounter more than one at a time.
Any of the later mercenary recruitment quests may qualify, although they give decent rewards. They are much more work than the mainline quests, force you to play in groups for much of it, and some of the mercenaries might not even be that desirable to a player depending on their preferred tactics. For instance, one set of mercenaries specializes in supporting either melee, ranged or spell-casting mercenaries. If you don't use many of one type, they won't do much good.
The most commonly cited though, is the Exorcist recruiting quest. People have noted that if you tried to do the entire thing from start to finish in one day, you'd probably run out of in-game stamina. This is widely considered to be almost impossible to do once you're out of the beginner's portion aside from the most aggressive power levelling. It does not help that the Exorcist is almost required for any high-level PvP. It also doesn't help that some of the enemies in one section of the dungeon are Immune to Bullets
Another strong contender is the Inventor. In order to start the questline, you need to have a Princess (another support mercenary) at least at level 50, then need to use her "Royal Signet" magic 20 times. The catch? Said skill only works on enemies using guns, a fairly rare occurrence until level 80, and since your Princess is probably going to be exactly level 50, most of the time she's going to get slaughtered before she can even use it on those monsters since they vastly outlevel her.
The lvl 120 upgrade quest would qualify as well. Absurd time limits, looting enemies that you have to kill twice, killing a boss that drains your HP with a high damage area attack, and a boss that can nearly kill your entire team in one hit.