Ear Worm: That theme which plays throughout the majority of the game.
Good Bad Bugs: The infamous coconut trick which allows to remove lots of enemies. There is even a glitch where you can get a glimpse of a final boss and remove all the enemies that way.
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Goddamned Bats: The airborne mine enemies tend to gather in huge clusters, just waiting to explode on you. And you really have to avoid that blast radius, too. They doubled as Demonic Spiders since you're a One-Hit-Point Wonder.
If you have them, you could easily take them out with either an Apple Jack or a Cotton Candy Copy.
That One Boss: The Beast at the end of World 2. It's a pain in the patookie for two main reasons: 1) The Beast is fast, agile, and adroit. The Boy is not. 2) No matter what he gets attacked with, the Boy dies in one hit, and if he does, then you have to start the whole fight over again from scratch. And you can't quit mid-fight and pick up there, either--if you want to stop, you have to go through the whole level over again.
In an article for Gamasutra, the developers themselves admitted that they didn't think this boss through enough. Oops.
It is possible to glitch the boss out and make the fight unwinnable by removing a spike ball. Normally they regenerate if they do not hit the boss, but when this troper played the level, he got all of the spike balls to disappear and the boss was still alive. He waited at each spawn point to confirm it.