This one sums up this series pretty well: One Gantzer is facing a powerful alien that is made up of several naked women combined together to form a giant naked woman. He gets pulled into her and is about to be crushed to death by dozens of naked women. So what does he do? He uses the last of his willpower to pull himself out, climbs up the alien, and forces it to give him a blowjob. Awesome. Also: Ewwww...
Not to mention that the act in question saves the guy's life when the mission's over.
In the dinosaur mission, Kurono managed to kill two fire spitting T-Rexes, a handful of raptors and a boss that gave Izumi a run for his money, all without his suit.
Given that arc lasted several volumes in total, it helps to be more specific. The definite highlight of that story (for Kurono at least) was when he fell off the bike right in front of one of the T-Rexes that had been chasing him. Everyone thinks he's doomed and screams for him to run. Instead, he remembers what he's fighting for, faces down the T-Rex and screams his defiance at it in an extended rant that makes it clear that, despite being at the time nothing more than a Badass Normal facing a giant fire-breathing killing-machine, he's not even considering the possibility of dying. Even the T-Rex is impressed. After that, even the actual fight itself can't compare:
Kurono: I'm immortal! I can't lose!! I'll never lose!! I am immortal! I'm immortal! Immortal! I won't lose! I'm immortal! Get over here! You can't beat me!! The one who will die is you!
The Old Man got his ultimate CMoAs in the same game. Although he'd already had a minor one when he tested the powers of the suit for the first time, grabbing a baby dinosaur (which still would have weighed several tonnes) by the tail and throwing it like it weighed nothing at all, at the climax of the arc he saves Kurono's life by grabbing the tail of the ultimate enemy in that game, the baby's mother which was over 100 meters tall and would have weighed well in excess of 1000 tons. Digging his feet into the concrete, he actually holds it in place long enough for Kurono to deliver the deathblow.
In the Dinosaur Arc, Daizaemon Kaze, without the use of his suit, started punching raptors to death.
Sakata's Dying Moment of Awesome in the Osaka arc (which doubles as a Tear Jerker). After discussing the implications of continued resurrection and deciding that if he dies he wants to stay dead, Sakata saves the group from Nurarihyon by holding it back with so much psychic power that his life force is burned out to nothing in seconds. And as the rest of the group scatters -
Takeshi beating up tons of aliens in the Osaka arc despite being a toddler with no fighting skills. Maybe he absorbed some residual awesome that Kaze gives off.
He's using all the same moves that Kaze does! Imitating his hero, Muscle Rider! That made it an /extra/ awesome CMoA.
The Nerdy Virgin (no name given) manages to survive the Italian Mission after all his teammates leave and is left with a little girl. He earns enough points to fulfill his promise of reviving Anzu.
Inaba finally gets his in the latest arc of Gantz by wiping out an entire wave of enemies and a sub-boss which have already been proven to be strong enough to easily destroy the strongest Gantz teams in the world. This wouldn't have been a big deal if it was done by Kurono but hey, come on, it's Inaba. Of course, being Gantz, this trope is horribly subverted and Inaba is crushed to death just moments after the rest of the group find him.
Not to mention the moment preceding it. Inaba is surrounded by aliens and faces seemingly certain death, when the old man leaps out of nowhere with guns blazing and sacrifices his life to ensure Inaba's safety and tells him to never stop shooting. Upon realizing that the old man was the only person in their group who ever really cared for him, Inaba steps up and starts mowing down aliens, fighting seriously for the first and last time.
Reika gets a very subtle CMOA in the latest chapter when she jumps from 0 points to 100 in a single mission, when most of the Gantz team didn't get a single point in that mission. Keep in mind that it's considered next to impossible to even get over 50 in a single mission.
Kurono reinforces his badass credentials when he single-handedly takes down a squadron of the giant aliens.
Until chapter 350 it looked like the giant skeletal alien... things were going to slaughter Clone Kurono and his team, but they only needed to find their weak spot to completely annihilate them in 15 SECONDS!
Made even more awesome: Kurono's old bully (who ended up with his high-school crush and casually rubs it in his face) asks him if he really entered the alien ship by himself and saved Tae. His bully calls him incredible, just for Kurono to respond: "Uh..Thanks".
The final battle of the manga ends with a titanic finish. Kei launches himself off the ground with such velocity that he headbutts the last giant with enough force to bash his skull open in one strike, killing him instantly. Upon seeing confirmation of the giant's death, humanity collectively celebrates, while the survivors of the battle make an epic escape via ships, once again enduring the lack of oxygen to get back to Earth while the alien mothership explodes behind them. Note that this is Kei's second time doing this. This moment is best viewed with "Rules of Nature" playing.
It's surely a crowning moment of something when Tae, completely helpless and seeing people dying all around her during Izumi's murderous rampage, sees a baby in a carriage (its mother dead nearby), picks the baby up without hesitation, and keeps running.
An eight-year old kid beating up a 30m alien with nothing but his fists.
When Sakurai, lamenting over his dead girlfriend, proceeds to use his Psychic Powers to tear apart a bunch of the invading aliens, who are just casually snacking on captured humans. Later on, the original Kurono single-handedly takes down a squadron of the invading aliens on their home turf, armed only with his Gantz gun and a katana.
Kurono's fight against the giant Buddha statue alien; when nothing else works, he super-charges his body and leaps from the ground straight up, flying into an open head wound (that he inflicted earlier) with such force he punches clear through its skull to start blowing up its brain inside its head.