Pretty much anything the masters of Ryozanpaku do when things become serious. Up to and including successfully fighting a fully and heavily armed military force during the Tournament Arc.
To elaborate, these guys were fighting soldiers in body armor with assault rifles, APCs, tanks, and gunships with their bare fists and legs (and katanas in Shigure's case) and were WINNING. To quote Akisame: "Be careful, even though they are wearing body armor, they can still die."
Kenichi's first use of the Mubyoshi punch vs Siegfried.
Kenichi elbowing a goddamned shark to save his sister during the Beach Chapter.
Mind you he only had a vague idea how to swim—he'd only learned that day—and he jumped off a cliff to save her
Kisara's overhead double kick to defeat Freya.
All of Hermit's battle with Berserker, especially this part, even more so than the "effort surpasses talent" speech.
Hermit: It's not that easy, Berserker! I'm not the kind of street trash you're used to fighting! I'm a trained martial artist who refuses to lose to the likes of you! I SWORE I'D NEVER GIVE IN! I PROMISED!!
Hermit's original Heel–Face Turn against Ragnarok while saving Honoka was pretty awesome too.
Hermit: "You owe me Shirahama! So do this for me! Kill Loki!"
The D of D tournament was a crowning moment for many of the Shinpaku members, my personal favorite being when Siegfried spun his head halfway around, and generally showed himself to be invincible.
I'd personally prefer he, being in Tibet doing hellish training on himself, sensing they needed his help, somehow got a old-style open cockpit single-person airplane, flying to the (extremely heavily defended) island, and then JUMPING to the arena from the airplane, landing unharmed, pwning some of their current enemies, then PASSING OUT from exhaustion from the 3 or so days that took him to get there, plus 40 days of spinning like a prayer wheel non-stop.
Not to mention the fact that he was SINGING on the way down.
Hell, he even stops dead in the middle of a battle...to compose music and write it out on the body of his opponent. He also has a Nice Hat.
Can we just agree that Siegfried is not a man, but an instance of one long continuous Crowning Moment of Awesome given human form?
Motion seconded, and carried.
He dodged missiles on his way down!
Let's not forget the bit at the end, where the members of the Shinpaku Alliance fight against Fortuna, an honest-to-goodness master-class fighter, and they WIN. Granted, it's shortly revealed that Fortuna was on the low end of the master spectrum, but it's still very impressive, as up to that point, non-masters even landing a blow on a master (much less defeating one) was completely unheard of. Oh, and pretty much all of them were suffering from their tournament injuries as well (at least 3 of them were completely bedridden before getting up to fight Fortuna), making it even more impressive.
Hermit's first usage of Kyousa was nothing short of awe. It severely damaged a low-class master, and he only learned the technique an hour or so ago. When Fortuna "no sold" the technique and backfisted Hermit away, he got up right back on his feet and made the most Badass Boast, "you're the one who's going to die!" A disciple saying that to a master. And Fortuna vomited blood like a broken fire hydrant.
This moment for Apachai , it turns out he was actually holding back in this fight and up until this moment was losing.
It's appropriately called the Punch You Don't Let Children See.
Heck, even Nijima gets some awesome moments, like when he used himself as bait to lure Berserker into a trap, or during the D of D Tournament where he enters himself as a fighter, despite having no fighting ability. He may be a Jerk Ass, but you have to admit that the guy has balls.
And what he lacks in martial arts skills he makes up for with tasers.
Also consider that he pretty much created the Shinpaku Alliance pretty much by himself, a feat made even more impressive by the fact that most of the members don't even like him, and didn't want to join. Yet he still manages to lead them.
He got another moment in chapter 55 when his group faced Hermit for the first time. After Hermit chucks one guy off the bridge into the river, Nijima (who has zero combat experience) sends the rest of the group back to base, deciding to face Hermit alone. He bluffs him until everybody else is a safe distance away, then jumps off the bridge, recovers the guy who got thrown off, and makes his way to safety.
Kenichi's latest escapade deserves mention just for the growth he's demonstrated. The first time he was fighting on top of a speeding vehicle, he was scared out of his mind and wondering just what the hell he was doing on top of the thing. The second time, when he's not yet reached Master-class... He tells Freya and Nijima to escape without them. He's got this. "This" being a bloody Master-class martial artist with a sword. As soon as the guy jumped onto the truck, Kenichi knew he was Master-class. He didn't flinch for a second.
The really amazing part is where he takes a blow on par with a blow which splits the truck they're standing on in half, and after seeing the carnage his Master-class foe causes, he tells Freya and Nijima to run, because, to quote: "I'll look after this! You two take Freya's grandfather and run!"
After the first 100 chapters or so, any time someone harms/threatens Miu. What follows is Kenichi taking Crouching Moron, Hidden Badass to the extreme.
Hayate Fuurinji, any time he actually decides to do something. Especially when he's training Kenichi, but he has other moments as well. "Play on land! Are you goldfish?!"
Don't count out the masters of Yami. First, there's Alexander Gaidar, who engaged in a sculpt-off with Koetsuji, and even used Koetsuji's techniques against him. Silcardo is a damn crazy loon who swallows pineapples whole. Diego... well, just look at the entry under Crazy Awesome on the main page. Agaard Jum Sai gets serious bonus points for managing to kill Apachai.
Kenichi uses Apachai's goddamn APANCH and CHAI KICK to defeat Koukin, complete with glowing eyes. Holy—
When it comes to protecting Kenichi from the aforementioned sword wielding master, now come back with a grudge NOT EVEN DEATH CAN KEEP APACHAI DOWN!!!!!
Actually, all of Kenichi's fight with Koukin is a Crowing Moment of Awesome. The two's fight is probably the closest thing of pure equals that has been seen yet.
Apachai then proceeds punch the guy in the face breaking his blade knocking him out the at two walls out the building AND HE'S STILL ALIVE!!!!
What follows is a triple-threat combination of Crowning Moments of Awesome, Funny and Heartwarming as Apachai tells Kenichi that he borrowed some time from the reaper in order to protect him. Cue Akisame showing up with Glowing Eyes of Doom and declaring that they will use their awesome skills to essentially cheat god and all the other masters chipping in to save the big lug. Yes, Akisame manages to be awesome, terrifying and hilarious at the same time.
Kenichi teaming up with Boris Ivanov to beat the high holy hell out of a bunch of Russian special forces soldiers who'd been sent to kill helpless students and teachers during a field trip.
Ethan and Rachel also fight off a unit of soldiers, though in their case, it's more that they don't care what Alexander Gaidar ordered, since he's not their master.
Tanimoto takes on more soldiers by himself, while Siegfried shows up to save the Shinpaku Alliance from yet another unit. These soldiers walked in expecting easy kills of a bunch of civilians (most of them kids) and had no idea what they were getting into.
Of all people, Ukita manages to save Chikage from being backstabbed by a Yami weapon wielder with a vajra by grabbing it with his hand, then proceeding to grab the wielder and toss him down upon the ground, instantly knocking him out.
Chapter 419 has the Shinpaku Alliance getting CMOA's but the biggest one has to go to Siegfried; all his opponent could say is what the fuckis this guy doing?
Sakaki gave a beating so brutal, Kenichi and Miu had to stop him, TWICE, and they were scared of "him" and he was on their side. Once against the French assassin and again against the political fighter, both master class
That's your evidence? What about when he took on two Masters from Yami at once just to keep Kenichi from being angry at him and successfully rescue YOMI member, Rachel Stanley?! Sakaki isCrowning Moment of Awesome.
Kenichi getting the ever-loving crap kicked out of him by the Valkyrie and GETTING UP LIKE NOTHING HAPPENED.
Actually, pretty much every time he gets up after severe butt-kicking is a CMOA.
Shigure vs. the Valkyrie gang.
Kenichi's father when he made his attempt to retrieve his son. He was willing to take on all the Ryouzanpaku masters AT ONCE with his rifle, managed to impress weapons mistress Shigure by doing a spinning, one-handed reload of the rifle he was carrying and FORCING her to dodge, and tore through every one of the traps near the hot spring. He was also willing to sacrifice himself to save his son by protecting him from an onrushing boulder.
Kenichi himself gets a moment right there when he shows his father how much he's grown by CATCHING the boulder as it threatened to crush them both. Sakaki had to save them a moment later when he started to lose his grip, but that didn't detract from the fact that he caught a boulder roughly five times his size.
To really understand how Kenichi's improved since he developed the Mubyoshi. When it was first made, he had to hold his hands against his target for several seconds. Now, he was able to pull it off instantly after being beaten around by Miu. As in, he was struggling to get up when he was last seen!
The entirety of Chapter 465. Kenichi and Miu (the latter having just been broken out of her brainwashing) take down Junazard's insanely-powerful swordsman henchman—and in the midst of it, Miu wards off the remaining traces of said brainwashing.
Chapter 466 has Furinji Saiga demonstrating exactly why he's the freaking One Shadow when he pulls off a Big Damn Villains moment, which includes stopping no less than three master class fighters in their tracks with his damn fingers.
Defeating three Master Class opponents by yourself without even breaking a sweat? It's been done. Dropping a jacket you were holding, defeating said three Master Class opponents, then CATCHING the jacket you dropped before it can fall? Now THAT'S Inspired!
Chapter 468: You're a Badass if you can casually do this.
Chapter 472: Jenazad demolishes Hongou so thoroughly that it's hard to see the latter pull a win against him.
Chapter 475: Hongo DOES pull that win against Jenazad—with his injured hand no less.
To elaborate: HE STRUCK THE ELBOW OF HIS INJURED ARM WITH HIS KNEE JUST SO IT WOULD HAVE THE FORCE NEEDED TO PULL OFF HIS ULTIMATE TECHNIQUE.
Chapter 490: Berserker catches a thrown shuriken with his teeth...then bends the weapon between his teethand proceeds to blow a gum-bubble through the shuriken.
Chapter 515: Ignoring his fight with Berserker, Kenichi, in response to Miu being hurt, Attacks Ogata Freaking Isshinsai.
Chapter 517: Ryuuto and Kenichi team up and Kenichi lands a glancing blow impressing Ogata. Turns out that was a distraction to create an opening for Ryuuto to attack his eyes, since his only moment of weakness is praising his apprentices!
Chapter 518: Ogata catching Ryuuto attacks with his teeth. Tsutomu saves Ryuuto and hit Ogata in the face while talking on his cell phone.
Chapter 524: A very dark moment for Isshinsai Ogata as he ends his fight with Tsutomu Tanaka by smashing his head into bloody paste with one elbow strike!
Tanaka also gets one when he sinks his teeth into Ogata's neck and draws blood right before said head-smashing.
Chapter 544: Touchuumaru sneaking into the Yami base single-handed... Is pretty much the low point of awesomeness in the chapter.
Sneaking in is nothing for Touchuumaru. THIS, however, is nothing short of awesomeness incarnate (and the Tempting Fate statement by the guards moments before seals it).
Of course Shigure breaking out of prison with just some needles and broken blade. All this while having her hands restrained.
Chapter 548: Koetsuji-sensei throws a Van going at full speed WITH JUST ONE HAND.
Chapter 577: The Shinpaku Alliance has joined forces with seven or so members of Yomi to fight against the apprentices of the weapons division. Two master-class weapon fighters show up, and things look bleak... and then Ryuto Asamiya comes in to help the good guys, too.