First of all, while this may simply become a list of each colossus battle, there's no rule that says that once a boss battle has been added, no one else can comment on it. Give your own take on a colossus battle, if you want, so long as it fits the criteria for this trope. You're not even restricted to the colossus battles. You might think some of the characters or the developers themselves are awesome, in which case feel free to add.
Lastly, a word of warning. Some of these examples might contain the strategies for defeating each colossi, spelled out and detailed. Some tropers may avoid doing this, but if you'd rather have the satisfaction of tackling the colossi first and working out your own strategy, read no further.
The boss battle against Avion, the fifth colossus. To be fair, it wasn't much while you were in the water, but the sight of Avion proudly soaring in and defying all the laws of physics (nothing that big and heavy-looking should be able to fly) with such gracefulness was rewarding on its own. The arena itself was the first most scenic, with the ruins partially submerged in the lake, and Avion perched on the tower, watching you swim by. Then, you get to see it fly around the arena. Eventually, you get to fly on its back, and that was where the awe in awesome comes in. The view: magnificent. The experience: thrilling. Colossus Climb over its wings and tail was amazing, going at such high speed up high. And this was the first boss that doesn't attack you on sight, so the moment of its death is more tragic than that of the other colossi so far confronted. Awesome in both senses of the word - impressive and full of awe.
In that same vein, Phalanx. The other flying colossus, this one both the largest, the most alien, and the only colossus that is completely harmless. Watching it fly around for the first portion of the battle set to a melancholy strings track makes it one of the most hauntingly beautiful encounters in the game. Little wonder why this fight is often singled out as one of the highlights of this game.
The very first colossus you fight is the first taste you get of what's to come, and it's awesome. If you're on your first playthrough, you've barely learned how basic platforming works in the game, and it leaves a lot for you to learn on your own. Learning the colossus' movements and how to survive its attempts to throw you off, followed by striking its weak point with amazing music in the background is absolutely breathtaking and adrenaline-pulsing. Once you've felled a colossus, you feel like you can take on anything.
Just the sheer size of the final Colossus Malus is awe inspiring. At first glance you think that you're looking at a mountain or an old abandoned castle but then when the massive rain storm starts up, electricity starts flowing down its arm, and those ominous eyes of dooms flare up you know you're in trouble. Once you've awakened to what amounts to a sentient mountain it starts throwing massive fire balls at you like they're going out of style, then you realize how terrifying this creature had to have been to the people that sealed Malus centuries ago for them to lock its legs in an eternal vice. More than any of the other Colossi Malus is the closest in size, power, and most importantly rage to Dormin, you face Malus last because he represents the absolute, complete, all-consuming rage of a god who was spited centuries ago when they forced him to be immobile and stuck to one place for all eternity. That is why the environment changes, the massive and violent storm is an outward manifestation of the storm raging inside of Dormin, Malus is truly the manifestation of malice itself.
Here's another way to approach Malus: you've come a long way. Fifteen Colossi the size of gods are dead by your hand. Your faithful steed and closest friend, Agro, has just fallen off the bridge that just collapsed behind you; verily, she was proud and strong until the end. But you know now that only one Colossus remains. You go up the stairs and see a tower stretching to the sky. "This is it," you say. "The final Colossus is inside that tower." Then the tower's spires begin moving. "...Or..."
This troper is always caught a bit off-guard by the battle with Gaius, the third Colossus. The first two are primarily learning experiences; yes, they can attack you, but generally you won't have any difficulty offing both of them, and it can be done without a complete understanding of the game mechanics (I know, because I didn't understand the mechanics completely by that point). When you enter Galus' arena and first see the size of him, you have to be in awe of the giant standing in front of you. On top of that, this is the first true puzzle boss, where you can't just jump on him and go to town. I always get nervous when I see him rearing back to strike at you with that big sword-thing on his right arm...