These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Awesome Music: Tons, but especially the epic final boss theme, and the cast theme. Nasty Gatekeeper's theme makes for a brilliant Oh, Crap too. The tribute album Secret Bonus Point only makes it better.
That One Boss: Treasure does everything to the Nasty Gatekeeper short of putting a sign over her head saying "this is That One Boss". The introduction, the music, and of course the difficulty (at least until you get the hang of it). then again, a little later on you get Twin Freaks which doesn't have the intro or music, but sure has the difficulty. Compared to them, the Final Boss is a cakewalk once you know how to fight him. Even before that there is, in the Unexpected Shmup Level, Baby Face, who puts you through laser hell while repeatedly reaching up to grab you with a hideous hand.
That One Level: Act 8, Scene 3. "Fun Forgiven" isn't too hard; it has the game's first potential of being squished, which is a One-Hit KO, but careful movements can keep the risk of that to a minimum. Then at the end, it has a bunch of Hangmans flipping in and out of usability with spike pits below. Unless you know what you're doing, this part can be despairing to get through.
Act 5, Scene 2, "Stair Wars" can be a troublesome level for some, since trying to hit Trouble Bruin while attempting to rise up a tower where the screen is auto-scrolling is certainly easier said than done. There's also a lot of potential for fury if Bruin randomly decides to do the move that doesn't put him in danger a bunch of times in a row.
Act 9, Scene 1. "Fatal Contraption" refers to Trouble Bruin's new machine, but should be referring to the rising platform Headdy stands on. It's mostly reasonable in terms of skill required, but through most of it, in stark contrast to the rest of the game, one mistake will squish Headdy, killing him instantly and taking him back to the start of the scene. Picked up the Melon Head? Yeah, you're dead. Raised the wrong ceilings where the brown rock enemies hang out? Oops, you've trapped yourself. Didn't jump at just the right time for that zig-zag run with the spikes hanging above? Headdy will jump backwards when hit by the spike, and get squished. That's not all of it either.
Unwinnable by Insanity: On the first real level, you have to catch a nearby platform to be able to climb a wall. As seen here, if you bring the platform too far away from the ledge or the other platform, you won't be able to continue. You can't move the platform again, and, provided you killed the only enemy around, you can't kill yourself, forcing you to reset the game.