The giant eel in Noki Bay. He's huge and you have to fight him in a dark, underwater trench. And he attacks by trying to eat you! Especially bad if you're not good with water.
Phantamanta. It's a large, paper-thin orange shadow in the shape of a manta. Wherever it goes, it leaves a trail of goop and emits a really creepy shriek when you try to spray it. The worst part? It's an Asteroids Monster and divides into smaller faster shadows as it is destroyed. When you've finally destroyed half of the original manta, the remaining mantas stop fooling around and all converge on your position at once with incredible speed at a time when you're probably almost out of health. You may think that going in the lake would protect you from it, but it just hovers over any water! Nowhere is safe!
A bit more meta, but the game uses bitmap images for generating goop on maps. The bitmap for an older version of Bianco Hill's goop shows what looks like a "Kug" (a Dummied Out enemy), a piranha plant, and... aNightmare Face with what looks like hexigonal teeth, big eyes, and a weird-looking wisp-hand sticking out. See it for yourself: here.
Try not to think too hard about the implications when Bowser calls Peach his wife. It's not true, but Peach seems...oddly complacent about it to say the least.
A few of the music and sound effects in Sunshine can be terrifying. For example, Hotel Delfino, a Hell Hotel-type ghost house stage, is frightening enough on its own, but its background music is a fairly standard-sounding tune...with bones rattling in the background.
Getting sucked into another dimension. You lose FLUDD, have only your jumps, are trapped in cheery, happy puzzle-worlds and the levels are Nintendo Hard. Hope you brought plenty of lives!