The use of "March" from the Nutcracker for a boss fight seems pretty random, awesome as the music is. It then does make sense when you realize the song's full name is "March of the Toy Soldiers," which fits the puppet-show motif very well and also alludes to an enemy found many times in the game.
The secret true final boss is a Corrupt Corporate Executive that attacks Headdy with money, and Headdy actually takes damage from touching it. Unlike the rest of the game, this encounter is happening in Headdy's real world, outside of a stage play. So it doesn't quite make sense for flimsy dollar bills to be hurting him, right? Well this scene has dialogue that's only retained in the original Japanese release, which reveals that the boss is the owner of the Dynamite Headdy stageplay and wants to work Headdy (and the series) to death with sequels for the sake of profit. These are the only things he says before throwing the money at you. Headdy obviously wouldn't want this, so by dodging the money, he's denying the deal and letting the series be as it is. And by touching it, he'd be taking the deal, thereby making the "bad" choice.
