The boss fight against Knuckles at Hidden Palace Zone. It's really easy, but what makes it so awesome is that you finally get revenge for everything he's put you through since you first saw him at the beginning of the game.
Drill Mobile battle at the end of Act 2 of Marble Garden Zone, Eggman uses his machine to destroy the stage itself around Sonic, dooming him to certain death. Tails, however, swoops in to carry his idol and chase Eggman down for a battle in the skies. Tails has very little stamina in the air in normal gameplay, and less so while carrying Sonic, but he hangs on for the whole boss fight and even manages to catch Sonic if he ever should fall, and then for good measure keeps going long enough for the sun to set in the background.
Really, the fact that Eggman destroyed the entire level just to kill Sonic is, in itself, a CMOA for both Eggman, who thought of it, and Sonic, who survived it.
All of Sonic 3 & Knuckles is a crowning moment for Eggman, simply due to the sheer amount of effort he puts into it from start to finish. In the first level, he starts a forest fire with Sonic in the middle, and then as soon as the hero escapes, cue an airship bombardment. And as awesome as Doomsday Zone was, the preceding boss fight featured Eggman piloting his gigantic mecha, Kyodai Eggman Robo, it is so titanic that its head almost filled the entire screen — and so did its laser beam, incidentally.
The fact that after reaching the end of Death Egg Zone Act 2, you have to fight a total of SIX boss battles (counting all the phases of the DEZ and TDZ bosses) is a testament how prepared, determined, and serious Eggman is in this game.
That he recovered, repaired, and launched the Death Egg twice in the span of just one game is a feat of awesome all its own.
What also makes this a CMOA for Eggman is unlike most of his plots, which are foiled by Sonic at the end of other games, the whole Death Egg saga takes from Sonic the Hedgehog 2 all the way to the Sonic & Knuckles portion of this game for Sonic to stop it completely. It took two games (or three if you consider the two portions of this title their own games) to completely foil this one plot, which proves how much a determinator Eggman can be. That, and he also managed to create Big Arm, a powerful mecha capable of knocking the rings out of Super Sonic if it got a hold of him. Too bad he did not account for something stronger than Super Sonic. Hyper Sonic, for example.
Doomsday Zone, where you fly through space as Super Sonic chasing down the ship, avoiding asteroids...
Temporarily defying Good Is Dumb, Knuckles gets his personal Crowning Moment of Awesome as he completes his Heel–Face Turn at the end of Hidden Palace Zone, coolly smashing the wall and leading Sonic and Tails towards Eggman. Depending on who you're playing as, he either collapses from pain and exhaustion or battles Super Mecha Sonic for the Master Emerald.
Knuckles punching the Chaos Emeralds right out of Super Sonic. Invincible Super Sonic Brought Down to Normal with just one punch.
Playing as Knuckles feels like a CMOA for him in a way, since his abilities allow him to explore whole new areas that Sonic and Tails couldn't access, and he battles and takes out tougher bosses, including Mecha Sonic in his Super form, making it feel like the character you're controlling is a whole level above Sonic and Tails.
Sonic's determination to defeat Eggman and stop the Death Egg once and for all (especially awesome in the Japanese S&K backstory, where we see him vowing that he won't rest until this one is destroyed). And the fact that he succeeded in the end despite everything Eggman and Knuckles threw at him over the course of the game, which included dropping him into a volcano and shooting the Death Egg's huge death beams at it.
Sky Sanctuary Zone: Chasing the recently revived Death Egg through floating ruins high in the sky as it escapes into space, and then succeeding in boarding it at the very last second just as the whole area crumbles under your feet makes for a very epic part and shows the title character's unstoppable determination and implacability.
Death Egg Zone: The ring shooter machines that send Sonic all over the place in neon yellow rings. They make another appearance in Sonic the Hedgehog 4.
Hyper Sonic, a fantastic reward for players who manage to collect every Chaos Emerald across both games. All the perks of Super Sonic (faster speed and invincibility), the Thunder Shield's double jump, the Fire Shield's dash, the Water Shield's bounce attack minus the bounce as well as the ability to breathe underwater...really, the only downside (aside from the obvious) is that the Thunder Shield's ring magnetism is absent, and even that can be arranged by just finding the shield yourself in this state!
Super Tails, especially when you unleash the Flickies. Just the mere fact he gains a super form after collecting all the emeralds accounts for this.
Hyper Knuckles, basically Hyper Sonic but every time he glides into a wall at a great enough speed, he causes an earthquake that destroys all enemies onscreen.