Incredible Crisis, a minigame compilation/widget game on the PS1, featured a very annoying level just before its halfway point where the player character has to match the weight of a golden piggy bank with the contents of her shopping bag, Indiana Jones style. Even worse, the player is given less and less time to solve the problem after each subsequent failure, and seriously, who the hell wants to do math in a party game?!
Even worse is the "final boss", which requires you to quickly tap the triangle and then X buttons to outrun a crane while using the D-pad to dodge bombs. At first it's just uncomfortable, but eventually it just gets painful.
Some of the minigames in Rayman Raving Rabbids can be annoyingly difficult, or just annoying. Like "Bunnies are Heartless to Pigs", where you have to guide a baby pig to its mother through a garbage dump, in which are hidden Rabbids who will jump out and torch you and the pig with a flamethrower if you run into them. The only thing guiding you is the sounds made by the pig (if it starts squealing, there's a Rabbid ahead of you), and you have to listen for them by holding the Wiimote next to your ear. Oh, and you have to do all this in 25 seconds or less. And later, you play a version with a Rabbid distracting you by blowing into an air horn.
Not to mention that the air horn version would often send too much data to the Wii Remote speaker at once and cause nothing but static or silence for... however long until you inevitably failed the minigame.
There was also the bathroom-door closing game. A lot of people had enough trouble with just closing the doors, but not me. Up until I got to the redux one.
Oh, and did you just so happen to get the PC version? Well, you won't have a problem with those levels listed above (the pig one is actually pretty fun when the sound is run through the regular speakers) but you will have a massive problem with the later, sheep-shearing one! It's either that it's just ridiculously harder with a mouse, or it's that it doesn't cope at all with lag (and it's the most computer-demanding minigame of them all), but it was outright IMPOSSIBLE for me! Also: ANY level that involves shaking the Wiimote is made FAR harder when you're using a mouse!
The ones where you have to guide a ball through a maze. Goddamn
The Crystal Challenge for the N. Ballism level in Crash Bash. Force fields which you can grab, but rarely spawn in your side (and when they do, someone else grabs it), and N. Gin showing up to shower your goal with balls, and his his ship deflects balls as well, ruining any chances you have of winning.
The sky ball level also has an over-the-top crystal challenge, in which there are red balls that kill you instantly if you touch them. They do no harm to computers, who will joyfully keep them in play even though letting them through doesn't subtract points.
Good luck getting relics (especially platinum relics) in any of the tank levels in the one-player mode. All three computers will gang up on you mercilessly and only blind luck can save you. Relics also require you to win twice in a row (three times in the case of platinum). The game goes up to Two Hundred Percent Completion for a reason. Fortunately, the two-player mode forces the computer to play on even 2 vs 2 footing throughout.
Given there's no such thing as a "That One Boss" tab for this video game genre, there's Big Bad Fox, a "Fox" (that is, tank minigame) type challenge against the Komodo Brothers. The less said about it, the better.
Riot Train in Sonic Shuffle is pure pain. The board is littered with rotating arrow spaces which can sometimes send you back in the opposite direction unless you land directly on them, which makes getting to the Stones rather tough. The train cars at the end can randomly detach and can end up costing you a turn if you're unlucky enough to be on one, and the final mini-game has you stopping the train via Button Mashing, but you have to be so freakishly fast that 99% of the time the computer will end up getting the emblem, so you better hope you got enough precioustones to make up the difference.
Nintendo Land's Pikmin Adventure attraction gives us Cage of Terror. Sure, it's one of the Brutal Bonus Levels, but it is significantly harder than the ones surrounding it. As the name implies, you don't so much proceed through the level as much as you kill the seemingly endless stream of enemies that are dropped into it. Including three consecutive instances of a Degraded Boss. When you think you're done, the level drops you into another arena, and the first thing you see are walls surrounding you... and an army of enemies immediately outside them... and then the walls lower. The only way to avoid damage here is to kill a few enemies VERY quickly, and escape through the gap you made. These are just two of the waves, this thing is a Marathon Level. Oh, and they throw That One Boss at the end because apparently Nintendo likes to see you suffer.