Pinball games can be tough enough on their own. Some games are difficult by design, some games are difficult due to operator settings and table configurations, and some are difficult if you aren't really good at them. Inclining a table by one extra degree or moving an outlane post two millimeters can be enough to turn a reasonable game into a beast.
SonicPinball SpinoffSonic Spinball is basically four gigantic pinball tables (all of them tough as hell, especially the last one) that all have to be beaten with no continues or passwords. Good luck with that.
Bally's Baby Pac-Man is notoriously hard for both pinball players and Pac-Man experts. Not only is the pinball table small and prone to drains, the player starts off with no power pellets or offensive capabilities in the maze game, the ghosts are more aggressive than in other Pac-games, and all of them can reverse direction at any time.
A trend with some modern pinballs is to have a reasonably-difficult table that's capped off with a final Wizard Mode that is insanely hard to reach. That keeps the game approachable for beginners, but makes it Nintendo Hard for the die-hards.
Stern Pinball's Iron Man has the legendary "Do Or Die Multiball" mode, which is nearly impossible to reach due to the difficulty of the goals needed to enable it — the player must beat the game's five main goals multiple times, and the game does not award any extra balls at all. Unfortunately, the mode itself is simply a series of ramp shots, making it an Anticlimax Boss for those who do manage to reach it.
Then there's "Valinor Multiball" in The Lord of the Rings, which rivals The Simpsons Pinball Party for the sheer difficulty of reaching it. It can only be enabled if the player completes all three multiball modes, achieving "There and Back Again", collecting all of the Gifts of the Elves, and Destroying the Ring.
This was a common complaint about The Lost World: Jurassic Park, as it followed the same progression system as Pinball Party (five modes, then the Wizard Mode) - which doesn't seem that bad, but every mode is rather hard on its own to clear.
James Cameron's Avatar is infamous for this, to the point where some players unfairly downgrade the game for its sheer difficulty. In addition to being a fast game that requires precise shooting skills, reaching the final Wizard Mode requires either completing the game's six main modes... or starting them on the same ball.
Hyperball, Steve Ritchie's attempt at creating a Shoot 'em Up pinball game, is notorious for being insanely difficult — which, coupled with its unorthodox gameplay, made it very hard to find public acceptance. Collectors universally advise turning down the difficulty to make it less frustrating for home play.