x1001,y1018: having no idea where the spiky tombstones makes an otherwise challenging puzzle downright impossible on the first few runthroughs, and there's no save nearby.
x997,y1017: as far as I can tell, this jump is impossible unless you do the tricky put-the-umbrella-away-before-the-double-jump which is very difficult on my crappy 2-key rollover laptop keyboard.
x9991020-x997: Three screens with with the most erratic, unfair monsters, and no save points because apparently Talps hates his players.
x971y1006: Three fires shooting at you from all sides, without any ability to dodge, and a hidden maze so you don't even know where you -can- dodge.
x971y1008-y1010: You complete a really difficult challenge avoiding 8 shooty fires, only to drop down into an instant-death screen with no way to save or avoid, except through trial and error.
x993y991-x991y990: The spike masher room is just... I mean look at it. There's no "safe zone" and I found myself believing it to be legitimately impossible the first two dozen times I did it. Plus I kept dying to the ninja-monkeys or the waterfall jump every other respawn which just made it extra frustrating, having no save right before the nigh-impossible sceen. Then you get through all that, only to die to some random erratic red guys just before you can save.
Finding the secret ending... never did. Even with the level editor, finding the way through that maze is borderline impossible.
Having to backtrack to each area 2-3 times with different items/keys to unlock doors.