The Climax Boss is the boss at a pivotal moment of the story. The Anti-Climax Boss is when that boss gets killed with about as much effort as it took to fight some of the tougher Elite Mooks. Or the first level Warmup Boss. Either way, there was a lot of buildup, and was expected to be a tense, critical, epic battle ended up being a breeze. Compare and contrast That One Boss, which sometimes causes the feeling that, at the end of the game, you have met an Anti-Climax Boss.