Opening moments of the first season, before the opening song, where Sousuke uses his Humongous Mecha to grab the Russian attack helicopter pursuing a girl, and then proceeds to throw it into the distance, where it crashes and explodes. Kurz is seen gloating about it only a little later in the episode.
In an episode of Full Metal Panic? Fumoffu, Kaname is being held hostage by a high-school gang. Sousuke tortures the details of the gang members' personal lives out of one of them, ties up the leader's little brother, and threatens him (and those close to the other gang members). The gangsters leave in a hurry, and the boy and Kaname are released from their respective captors. The best part? The kid had been bribed to be a decoy.
Tessa's moment is foiling Gauron's takeover of the de Danaan in the last arc of the first season. As soon as he's taken prisoner, she makes sure to deactivate the ship's warheads just in case something goes wrong; when it does, she takes the risk of using her Whispered powers to communicate with Kaname, then grabs a gun and unloads it at Gauron to give Kaname a chance to run for it. She continues to stand up to Gauron as the rest of her plan unfolds, fearlessly mocking him even with half her face covered in blood from a Psychic Nosebleed, taking advantage of the US Navy's own security protocols to keep the de Danaan from being torpedoed, and generally proving in detail why she's the captain of a highly advanced military submarine at the age of seventeen. Badass.
Al, the Arbalest's Artificial Intelligence, not only developing a better sense of humor than Sousuke has, but also matter-of-factly acknowledging that the Arbalest doesn't work correctly - then pointing out, equally matter-of-factly, that this is because Sousuke is part of the Arbalest's systems, and the Arbalest isn't going to be able to work properly until Sousuke gets over his own issues enough to operate it correctly. What would be a piece of good sense coming from another character is a genuine Crowning Moment of Awesome when it comes directly from the very Humongous Mecha that Sousuke just called a piece of garbage.
Meanwhile, Kaname's Crowning Moment comes in The Second Raid: left alone and vulnerable after Sousuke is forced to give up acting as her bodyguard, she succeeds in outwitting both the Mithril Intelligence agent shadowing her and the professional assassin sent to kill her.
She follows it up by making the Intelligence agent take her to Hong Kong so that she can deliver an epic Get a Hold of Yourself, Man! to Sousuke, snapping him out of the Heroic BSOD he'd been in for half the series just in time for him to deliver a Curb-Stomp Battle the likes of which is not matched anywhere else in the series.
And how she does it, man! "Everyone's in danger, right? Not to mention your class credits! Now MOVE YOUR ASS!!!"
In The Second Raid, Sousuke takes on five Lambda-driver-equipped Codarls, by himself, with minimal armaments. He finally managed to make the Lambda driver work when he wants it - and not only make it work, but completely obliterate Gates's Codarl right through Clouseau's M9, which Gates is using as a shield, without touching the M9 at all. Epic is truly the word.
Even more so when you consider that he took down the first four within a minute. When you see that in the first series, he struggled for minutes against just one, this is truly badass. The full list:
Shot two while falling upside down. The second is just plain brutal as he used a billboard as a stepping stone. A billboard. For a mech weighting several tons. And it didn't get crushed (until a Codarl tried to do the same move, anyway).
Shot one in two (literally) mid-air, nothing fancy.
Ensnared one with a cable and pulled it down to ground level where the cable snapped and the Codarl blew up.
And of course the aforementioned badassery where he literally blew Gates away without line of fire. Clouseau must have soiled his pants right there and then. "I know I told you to believe in your abilities and all... but that was overkill, sergeant!"
Gates: "You bastard! Who the HELL are you?" Sousuke: "Who am I? If you really want to know, I'll tell you." Cue Minami Kaze "I don't give a damn about Mithril. I am from Jindai Municipal High School class 2-4. My student number is 41. I am in charge of garbage disposal and umbrellas. My name is Sousuke Sagara!!!" (Cue Lambda Driver powered Megaton Punch).
Also, making that line sound Bad Ass has to be a CMOA in itself.
Speaking of Bad Ass lines, similar to that CMOA one, his much earlier response to a mook's generic "Who are you?" question in the first season. "I take out the trash." Refers both to his class assigned duty and his military job.
In Continue On My Own, in order to make their escape from Merida, Tessa orders the Tuatha de Danaan to fucking RAM at an attacking Benemoth AT FULL SPEED. It completely caught its pilot off-guard (though Clouseau and Kurz helped) and the huge AS collapsed.
Burning One Man Force. Sousuke defeats a recently capturedM9. With an modified RK-92 Crossbow. The match badly damaged it, but he proceeds to face TEN armed to the teeth Arm Slaves. With just a Heat Hammer at hand. And wins.
During ''Come Make My Day'' or chapter 41 of the manga Full Metal Panic Sigma, Sousuke gets reunited with his Nakama, Mao & Kurz while they were both assaulting Leonard's lair only for them to be confronted by Codarls/Venoms. Do remember these guys are packing Lambda Drivers than can bend the laws of physics & tear apart anything that gets in their way while the team is just piloting normal ASes. So what do they do?? Do a seriously Bad AssCombination Attack to take advantage of the LD's weakness of only being able to focus their power at one side at a time & decisively kick their asses. Not to mention that the nameof the attack. Seriously, thebattlehastobeseen to be believed.
From the same book, the debut of ARX-8 Laevatein. It handed 3 Codarls and Benemoths' collective asses SINGLE-HANDEDLY, in FIVE minutes. (Though the time is a bit longer than AL expected.)
In the tenth light novel, Approaching Nick of Time, Kurz Weber gets his moment: sniping his former mentor Wilhelm Casper in order to save Sousuke and Tessa - in the process breaking a record set by Casper, which Casper had previously told him he would never be able to match. If that weren't enough, he accomplishes it while dying from the horrific injuries he suffered when Casper destroyed his M9, including crushed legs and a broken back.
The last novels, Always Stand By Me, has many CMOA to list, but one of them deserves a special mention: Sousuke destroys Leonard Testarosa's Belial. WITH M72 LAW. Now one should remember that Belial is able to tear Arbalest apart without trying, and still gains upper hand (and close to winning) when facing Sousuke's ARX-8 Laevatein. He destroys it with a MAN-PORTABLE WEAPON.
After that, AL, the AI of now-trashed Laevatein, defies usual norms of "only humans can activiate Lambda Drivers" and activiates the barrier by itself. To stop an INCOMING NUKE.
Also from Always Stand By Me: typically stoic Sousuke finally lands on Meridia Island. Opening a radio channel he has this to say:
You think I've come here in a combat-ready AS to start pleading with you to stop? Don't make me laugh. I've come to be as much of a pain in the ass as possible. Good, they must all be hearing this by now. So, listen closely - [he paused to take a breath] - I'm going to crush you all.
My specialties are arson and demolition. I'm going to turn that occult machine you're worshipping into a pile of slag in five seconds. Come on, I want to hear you plead "Please don't! These are our hopes!" I want to see you whimper and hide, crying "oh this cruel world has hurt us so much, we want it to disappear! That would be a sight to remember. I'll record it and transmit it for the world to see. I'll make you into a public joke. So get ready - I'm coming for you!
Before this, the flight towards Melida island. Laevatein + XL-3=fireworks upon Amalgam's defences.
How has no one mentioned Kazama's epic moment in Fummofu? When he takes Kurtz's gun and runs up a hill shooting all the security guns. Turned into a crowning moment of funny when he jumps the fence and gets a faceful of Sosuke dick...
A villainous one for Gauron occurs in the first season, when he uses his suit's Lambda Driver to disintegrate a charging Humongous Mechawith a Finger Gun gesture. Talk about adding insult to injury.
An episode of The Second Raid had a Mithril mission in Nanjing being hampered by the fact that their communications guy was The Mole, feeding their transmissions to their enemies so they always know what Mithril's going to do. What do Tessa and Kalinnin do to solve this? Remind everyone of an offhand remark one of the team made during the briefing where the communcations officer wasn't present, signaling everyone to do the exact opposite of what Kalinnin is ordering them to do. This results in the leader of the bad guys being tricked into a trap, from which he only barely escapes thanks to his Lamba drive and a well-placed mine
When Sōsuke fights five Venom units in the finale, and singlehandedly hands their asses to them, when at first, he had great difficulty in defeating even one.
Sousuke: Kashim... YOU AREN'T MY FRIEND!! DON'T CALL ME THAT, YOU SHITHEAD!!!
The last two episodes of the first season is just one CMOA after another, with each major character getting their shot. The best may be Tessa's, who stops Gauron's plan by taking control of Dana back, managing to save the TDD-1 from not one, but two incoming torpedoes with ONE manuever, all while in a mind link with Kaname, to help her meld with the ship, and inform her of what to do after the meld is made. The look on Tessa's face when she confronts Gauron after all of this, while blood is running down half her face, is pure awesome.