There was the BNK3R boss from Borderlands 2, that boss fight the first time through was nothing more than a clusterfuck. I'd either be trying to hit his absurdly small weak point while he kept swaying from side to side, or sprinting across the arena while it kept exploding like it was the surface of the sun, or Brick constantly screaming "AAAAAAAAA MORTARS MORTARS MORTARS AAAAAAAAAA" into my ECHO.
There was also this dude in Batman: Arkham City, this ONE DUDE during the expert Funhouse combat level who during the first wave would run over and pick up this fire extinguisher and if I didn't stop him he'd hurl it at me while I'd try to take down the one-armed lieutenant, and then the smoke would clog the screen. I could see but the lieutenant would spaz out and swing his hammer in a way that was impossible to predict and I'd get my combo smacked straight down to zero.
Finally, in WoW during patch 4.2 where you had all those Firelands dailies, during my quests onto the floating island to the west side of the map, there were these rock elementals who had an absurdly large aggro radius and would interrupt whatever you were doing, forcing you to kill them and pray he had no friends nearby.