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.
Contested Sequel: StarTropics II was about time travel rather than messing around in the tropics, and some fans of the first game didn't like the change.
Demonic Spiders: Those freaking gas mask robot raygun alien things in the last two levels of the first game. Durable, damaging, long range attack... argh.
Ethnic Scrappy: Baboo. The developers refrained from giving him a goofy accent, but appearance wise he's practically a caricature of a native islander. Fat, wild hair, grass skirt...
Fridge Logic: If Dr. J is such a good friend to the villagers of C-Island, why is his lab on the other side of a cave full of monsters from their village?
That cave wasn't always full of monsters. It's suggested that prior to Dr. Jones's kidnapping, it was just an ordinary cave with only tame creatures in it, and whatever kidnapped Dr. Jones also caused the monsters to appear in the cave.
That may justify the monsters, but it doesn't explain the deathtraps.
Goddamned Bats: A lot, especially in the sequel which has numerous flying enemies, enemies invulnerable to frontal attacks, and especially the damn slimes that jump diagonally.
Nightmare Fuel: If you get too greedy in the first treasure/potion room in the Island Tunnel, you'll end up drowning in a room full of water with bones and skulls floating in it.
Ship Tease: Mica tells Mike in a backwards message that she'll be thinking of him just before she returns to her home planet with her people. Think she abducted Mike for their wedding?
That One Attack: Zoda-Y isn't particular difficult until he turns into his owl form, where his feather attack becomes an absolute nightmare to dodge (it doesn't help that it's also pushing you backwards into a nearby row of spikes at the same time and there might be bats to contend with if you haven't killed them all.) Needless to say, you'll probably be burning through most of your health potions in the Boss Rush on this segment alone.
The Knight Rider, the boss of the first dungeon in chapter 8 of the sequel, is a major pain to fight. He moves quickly back and forth across the room while you're on a rapidly moving conveyor belt trying to shoot at him with limited range weapons.
The Dragon, which you have to jump to hit, can fly around blanketing the room in flames, and has to be fought under a time limit.
Chapter Three runs you through a series of five consecutive dungeons with few healing items. The longest and most difficult of these is the Ghost Village, which also includes several false exits to further vex the player.
After leveling out a bit for a couple chapters following Ghost Village, the difficulty spikes once more in Chapter 7, with enemies suddenly dealing much more damage and able to hit you from a far greater range due to being equipped with ray guns and other such weaponry.
The first dungeon of Chapter 8 in the sequel. There may be a lot of health potions, but you'll sure as hell need all of them because there's no checkpoints, and it's the home of the Knight Rider (see That One Boss above.) Not to mention the section that sticks you on a fast-moving conveyor belt and forces you to speed your way through forks in the road to avoid running into giant spikes and get through fast enough before you have to take even more damage to get across expanding spiked floors.
They Changed It, Now It Sucks: The Happy Video Game Nerd makes the argument that the changes in the control scheme from StarTropics to Zoda's Revenge is one of the reasons the game is horrible (at least, in his opinion; he acknowledges in his Zoda's Revenge review that just as many people disagree with his opinion as agree with him).