Let me define a mini-game for you at the outset. It's when some sort of mechanic or goal in a video game is introduced as a new challenge for a short time which may or may not be instrumental to continuing the progression of the game and has little to do with the majority of the way the game is normally played. You're running around mowing down murder mutants in a first person shooter, then suddenly you have to win a dance contest by mashing buttons to a rhythm. That sort of thing.
There's nothing wrong with mini-games. If Square Enix offered an updated version of the Mount Condor levels from Final Fantasy VII for iOS I probably wouldn't play anything else. That said, sometimes games drop the ball on these little diversions. And sometimes they don't so much drop is as inspire a player to go after the ball with a filet knife until it's a pile of rubbery shreds still warm from the rage of the frustrated.
These are those ball murderers.
10. Breath of Fire III (The Black Ship Boost Counter): In order to get the Black Ship's guidance system working you have to activate the boost counter. This involves having Momo stay at the bridge, you walking through a maze to where the boost counter is and checking the number on it. When you leave the room to go back to the bridge a beeping starts, and you have to keep track of it by counting up from the last number you read, as you go through the maze, and talk to Momo exactly when the count reaches 100. The only way I have ever been able to do this properly is by having another person come in to help me keep track of the beeps while I navigated the maze.
9. Doctor Who: Eternity Clock (Perception Filters): Really this applies to any puzzle in a game that involves rotating different portions of a picture to create a whole, but the ones on the hard setting on Eternity Clock really take the cake. You have to align the picture by rotating concentric circles, but each circle also affects other circles. You basically have to solve these things with a pen and paper. If I wanted to do that I'd play Dungeons and Dragons.