Rave Master/Awesome

In the vastly underrated shonen action manga Groove Adventure RAVE aka Rave Master, the titular Rave Master Haru Glory and his True Companions run into another group of oppressed warriors who ask him to help them defeat an army of 1000 demons, apparently led by Haru's missing father, Gale. Uncharacteristically, the usually unfailingly altruistic Haru refuses to ally with them, causing everyone to wonder What the Hell, Hero? while Haru disappears somewhere. While his friends have no idea where he's gone, we find out in short order -- he's gone to challenge the entire army by himself. The scene where he ploughs into the ranks of the army, outnumbered literally 1000 to 1 and storms through their ranks in a berserk rampage solidifies Haru as a grade-A Badass. Especially since he WINS.
After a looong stretch of near-uselessness, Elie finally got one in volume 23, where she's entered in a dance competition. A pair of somewhat important minor characters dancing before her get 96 points, then the Dragon Dancers Let and Julia in disguise get 100. Elie's partner disappears on her, and while she waits for him, the band decides to play a song they once did for Resha Valentine, with whom Elie has a "mysterious connection." The song taps into that connection, and Elie's ensuing solo dance enchants the entire town, not to mention the giant snake, provokes Iulius' Heel Face Turn and incidentally earns her a whopping 999 points.
- She gets another one in volume 28, when she finally harnesses her Aetherion powers to blow a hole in Endless and then banish it from the Mystic Realm, with the help of Belnika and the time-space staff.
  - And another in volume 31, after she has regained her memories of being Resha Valentine and returned with Haru to the present, she channels her Aetherion power to defeat Shakuma Raregroove, the most powerful sorcerer in the world. Sure, Haru lands the finishing blow, but it's Elie who really shines in that fight.
  - Shame it took Elie so long to live up to her original Crowning Moment of blowing up an entire dog racing stadium building with her tonfa blasters in her debut in Volume 2.
In volume 27, Let takes on Hardner, and initially looks like he's got the upper hand; however, when Hardner has got his second wind, he uses his Dark Bring to restore every wound Let has ever sustained. As Let lies there, apparently paralyzed and at death's door, he hears a dragon's roar, which informs him that his girlfriend, Julia, has beaten The Dragon (no pun intended). His response?

Let: Julia was victorious. [finger twitches.] Then I suppose I should get up ... and defeat Hardner.

- Sure, he got his butt kicked in short order, but the mere fact that he managed to stand up let alone fight, secures his place in the halls of Badass. Plus, in the next volume Haru reveals that Let wore Hardner down sufficiently for Haru to provoke a Phlebotinum Breakdown and defeat him.
- Earlier, when the gang takes on the Oracion Six, Let (then still a dragon) is taking on Jegan, who pretty much whups his ass. It's then revealed that the Dragon Race can either live life like Let (half-human, half-dragon), or try to conquer their dragon half and become human. It has an astronomically low success rate, and if it isn't done in a special temple, that success rate dips even lower. Let tries it without the temple. He succeeds.
Haru got another towards the end of Volume 29, just after Shiba's death. The rest of the True Companions are surrounded by the bug army of the demon Berial, and apparently in for the fight of their lives. Then Haru arrives, carrying Shiba's body, and apparently ignoring Berial and his army. Haru lays it down, and then says "I wanna bury Shiba. So get lost. Now."
- That would be Badass enough, but immediately afterward, he pulls out his sword and starts laying into the villains. Berial starts posturing, saying "Now I get to show you the real power of my Dark Bring." Haru promptly cuts him in half.
- Yet another for Haru. In volume 31, Haru has been shifted 50 years to the past, and--due to his own time-meddling--a group of Raregroove mercenaries have kidnapped Resha Valentine. Haru chases their carriage, even when his Speed Upgrade Sword begins to fail on him due to Resha's danger. Just before his sword shorts out, he grabs the carriage door, catches a crossbow bolt between his teeth, grabs onto a trailing rope as he falls out of the carriage, snaps the crossbow bolt as he pulls himself back towards the carriage, and then, just as one of the Mooks cuts the rope, takes a final leap and plants his fist right in the Mook's face.
Musica gets one in Volume 32. Realizing that Haru needs his own personal sword and discovering that his grandfather's too frozen-by-a-demon to do the job, Musica decides on no previous experience to forge Haru's sword himself. When the first attempt (forged from the last ingot of the Unobtainium the original Ten Powers was made out of) shatters, Musica picks up the still burning pieces and reforges them. And again. And again. Finally he realizes that Haru's sword has to be personal to both of them and adds some of his special silver to the mix. The ensuing firestorm "mightiest of all swords" and defrosts the whole town. Musica, however, has exhausted all of his energy and collapses, apparently Deader Than Dead. However, when Haru appears on the scene, he yells at Musica not to die. Cut to Musica having a Near-Death Experience with his really-dead love interest Reina, who gives him the traditionally "You're not ready to die yet, go back and live, idiot" speech, and he comes Back from the Dead. He collapses again just after handing Haru his sword, but tells them "Relax ... I'm not going to die. The lady already laughed at me once."
Then there's Sieg Hart who's practically a walking Moment of Awesome. The very first thing he does after his reappearance is to make whole Oracion Six (who were at that moment beating the everloving crap out of Haru and his crew) run with their tails between legs. He later tops it off by defeating no less than 1000 mages using only his sword while taking care not to kill any of them, and immediately after that fighting Haja (his equal in magic who additionally possessed Dark Bring granting him limitless magical supply) for seven days and nights and in the end killing him with a perfectly mundane stick. That's how he rolls.