Yzak's semi-Heel Face Turn in the final episodes. He manages to kill two of the three Druggies singlehandedly; once saving Cagalli, and the second time in defense of Dearka. The second time is particularly awesome, as he mostly sounds pissed off while he's doing it. "GIVE ME THAT WEAPON!" *takes BFG, fires.*
Yzak rescuing Cagalli deserves elaboration. Cagalli is ambushed by Super Soldier Shani Andras, who sends a beam of hot plasma at her. Cagalli's about to be toast, when Yzak throws his own mobile suit in front of hers and takes the beam on his shield. Said Big Damn Heroes moment would probably be plenty awesome by itself, but then he draws a beam saber and charges the enemy Gundam head-on. Shani opens fire again, blowing Yzak's shield into a million pieces and engulfing his Gundam in a huge explosion. Cue a moment of horrified silence...followed by the Duel burstingOut of the InfernoDual Wielding beam sabers. Before Shani can say "holy shit", Yzak chops the arms off his Gundam with one saber and rams the other through his cockpit. Bad. Ass.
Not to mention he also blew up the ship commanded by Captain Sutherland - member of Blue Cosmos, Azrael's dragon and mastermind of the JOSH-A cyclops trap - by firing a grenade from his beam rifle's underslung launcher straight into the bridge. Bitch got noob tubed!
In the original Japanese, the line is much more understated; his voice actor delivers his catch phrase almost casually and with a quiet chuckle: "Heh, I knew that I could make the impossible possible..." It's possibly even more epic that wa.
Mu already has one by the time the series starts. To elaborate it was considered at the time that five mobile armors were needed to take down one Ginn. Mu took down five Ginns with one mobile armor. This feat was so awesome that he was famous in OMNI and ZAFT and known as "The Hawk of Endymion."
Mu La Flaga repeatedly fighting Humongous Mecha and Bigger StickHumongous Mecha in either his Moebius Zero mobile armor - which, while orders of magnitude better than the production model Moebius mobile armors to the point that Mu is one of the only two living OMNI pilot who can fly it, is still pretty puny by comparison to even a standard mobile suit - or a simple fighter jet.
During episode 5, Kira's mobile suit runs out of power. He could recharge the power by going back to the Archangel and getting another Striker pack, but he gets captured by a ZAFT Gundam. So what does Mu do? He dives in with his mobile armor, blasts the Gundam enough to get it to drop Kira, and has the Archangel load the replacement Striker pack onto the launch catapult and shoot it out to Kira. "Making the Impossible Possible" indeed.
In the same episode as the above Launcher Striker Pack stunt, Mu makes a solo run on Le Creuset's flagship in his mobile armor and forces it to withdraw. Bear in mind that this is the same guy who has a psychic connection with Mu, so even with forewarning, they still couldn't avoid damage.
He gets one earlier than that. During episode 21, while fighting BuCUEs (canine-esque mobile suits) he throws a beam saber into one's eye and then kicks the head off another.
Some fans even argue that he gets two other CMoA's. All three times being when he has to reprogram the X-105 Strike's Operating System... In the middle of a battle. While being fired upon. The first of the above-mentioned are in the beginning, when Kira takes over the X-105 Strike and can't control it, because the OS is messed up. He reprograms the OS in less than 2 minutes and goes on to kick ZAFT ass in a Mobile Suit he's completely unfamiliar with. To reiterate: He reprogrammed an entire OS, probably as large as Windows 7 if not larger, in less than 2 minutes. Even if he IS the Ultimate Coordinator, it is still highly improbable that a teenager who has no experience in programming Mobile Suit OS's can reprogram it in such a short time.
Kira actually has experience with programming mobile suit OS' If you recall in the first episode it has him running and programming data for a new OS for a mobile suit like object. It is also mentioned that Kira had been helping him for quite some time as he carries data for it around. Doesn't make it less assume.
The other time, he does it while being stuck in the sand, again surrounded by lots of ZAFT Mobile Suits intent on killing him.
Natarle manages to gain the upper hand with the Dominion against Murrue's Archangel, proving that she was the one who had things together back when she served on the latter ship.
While not having to do with fighting, Lacus herself gets a few. Her first one is when she demands Rau withdraw from fighting the Archangel after Kira frees her. Up until this point she's come off as an Idol Singer with a touch of Cloud Cuckoolander, and has never raised her voice once. To suddenly hear her yelling at Rau for trying to start a battle is pretty awesome. She also manages to organize a resistance movement within the ZAFT military, give Kira the Freedom with relative ease, and then steal the new battleship ZAFT had been developing. For a total non combatant Lacus arguably makes as many contributions to ending the war as Kira does.
For this troper , Lacus and the Clyne Faction HIJACKING A WARSHIP was epic win.
Episode 49 also sees a small but noble one from Fallen Princess (and recovering former Yandere) Flay Allster, now one of the Dominion'sBridge Bunnies. Upon hearing that Azrael wants the Archangel destroyed, Flay decides to screw authority and tries to warn her former shipmates. If this doesn't seem awesome, recall that Flay is really just a teenage girl in way over her head, and Azrael is in the middle of a huge Villainous Breakdown and threatening to shoot people who disobey him.
And that Azrael, as soon as he hears Flay's broadcast, grabs the kid by the arm and bitchslaps her around in mid gravity, while still screaming his head off. Seeing him abuse her bridge bunny for doing the right thing is what finally gives Natarle the Heroic Resolve to screw Azrael's authority, send all of the bridge bunnies away and pull the aforementioned CMOAs.
Natarle's sacrifice is made still more awesome due to Azrael's reaction. Just before firing on the Archangel, Azrael was ranting about how "I can still win; I always win." After Mu's Heroic Sacrifice, when Azrael sees that the Archangel is still standing, Natarle just gives this little smile and calmly states "You lose." Seeing one of the most heinous bastards in the show staring at the oncoming positron beam was very, very satisfying.
And then there's Magnificent BastardRau Le Creuset in episodes 49 and 50. Kira and Athrun have been kicking ass using massive gunships attached to their mobile suits. Then Kira decides to attack Rau...who proceeds to tear Kira's gunship to pieces without getting scratched.
Rau gets another CMoA at Mendel, when he doesn't just fight Mu's Strike Gundam with a GuAIZ, he beats him with it, simultaneously demonstrating the GuAIZ's power and his own badassery.
One earlier than that (and this one kind of a Crowning Moment of Evil): during episode 37, Fllay has Rau at gunpoint, and has a pretty good chance of killing him. Rau proceeds to utterly destroy the poor girl's sense of purpose and leaves her unable to do anything, without so much as rising from his chair.
Dearka has a few. In the medical bay, his hands tied behind his back he is attacked by two angry women, the first with a knife and the second with a gun, both intent on killing him for different reasons. He survives with nothing more than a cut above his hairline.
Later in a cell he sees the first attacker, who he had teased about her boyfriend dying. He asks about how he died and finally concludes "It's not me."
It is this troper's opinion that Athrun ripping off Tolle Koenig's head BY THROWING HIS SHIELD at the Skygrasper counts as a CMoA for him. Actually, pretty much all of that episode is one massive CMoA for Athrun, as he handily kicks Kira's arse all over the place - with the latter only being saved from total annihilation by the Aegis's battery conveniently running out.
Sai Argyle gets his when he not only saves Dearka from Miriallia (preventing her from committing a war crime in the process), but then proceeds to lay the verbal smackdown on Flay, finally putting her in her place, and triggering the start of her Heel Face Turn.
As only natural for a Gundam series, there is lots of Awesome Music to go around, but the fourth OP is especially an example of Crowing Music of Awesome.