Rio in Spiral is introduced with a string of these. First, she lures a teacher to his death (thanks to Adaptation Decay, either by falling down and stabbing him when he helps her up, or packing a sloped room with melting dry ice and watching him suffocate at the bottom while she stayed clear of the fumes at the top). Then, she builds a bomb, hides it in a stuffed toy, and brings it up to the room where the Great Detective already expects her to kill his Sidekick—only, instead of building a bomb big enough to kill, it's only enough to seriously injure herself and obscure the distinct physical marking that would identify her as the killer. Finally, when they approach her in the hospital, she's prepared a game: by blowing herself up, she's established herself as reckless and willing to throw her life away. So she tells him that the winner will be the one who can believe in himself, and her companion brings in two glasses of water. She says that one contains an extremely bitter poison called Strychnine, and the other plain sugar; as the two are identical, she doesn't know which is which. She and Ayumu must each drink one, and whoever lives is the winner. Ayumu seemingly identifies the trick, and claims they're both sugar... but the water in his glass is bitter, and it barely touched his tongue. While he's going through his Heroic BSOD, she calmly drains her glass and her companion notes for the audience's convenience that Rio was correct about the winner needing to believe in their abilities: there really was no poison; it was just an extremely bitter cold medicine.
And cue Hiyono the Neutral Female stomping forward and draining the glass herself, proving Ayumu's original theory correct, hitting Rio's weak spot by calling her a coward for lying about being willing to risk her life, and getting Rio to confess to the original murder. On tape. This in turn sets off Ayumu's own Crowning Moment Of Awesome... but your life has been ruined enough.
The manga has quite a few more Crowning Moments of Awesome, though the two listed above were, indeed, awesome. Kanone has one later in when he lets Hizumi kill him, to accomplish three things: Screw Destiny, something he's been trying to do since he showed up, pull a very impressive Mind Screw on Hizumi, and give Ayumu "hope" (something he's usually in desperate need of).
Hiyono gets some epic moments in the manga, between getting information and blackmailing people, but especially during the Kanone arc. She's supposedly playing the role of decoy against Kanone, who will not kill "normal" people. First, she stalls him long enough for Ayumu to think up a plan, by cutting her own wrist and blocking his way until she collapses from blood loss, forcing Kanone to treat her so she doesn't die. He then sees through every plan, trap, and trick that Ayumu, his sister-in-law, and the Blade Children working together throw at him, until Hiyono shows up with a tranquilizer gun and shoots him, which he technically *did* expect... except that she was wearing a pair of giant cat ears on her head, which threw him completely off-balance. Yes, the one and only battle in which cat ears were the deciding factor. Remember, this is after she had collapsed from blood loss.
Madoka gets hers when she goes all Mama Bear on Kanone for messing with her adorable brother-in-law—for that matter, Kanone is pure awesome in this fight, too. She's a cop, he's a highly trained fighter, they're shooting and throwing knives at each other, and Madoka is doing this in a skirt and high heels.
Ayumu becomes kind of a walking CMOA when he starts tidying up the absolute mess that the series is in the last two volumes, absolutely refusing to break down like he did all the time in the beginning, and even sometimes smiling. (Remember Ayumu is/used to be the worst no-self-esteem brooding angstbucket in the series.) That, or the calm with which he does it all can just creep the hell out of the reader.
The series being loaded with awesome female characters, any occurrence of girls fighting, alongside or against each other, without anyone pulling any punches. This troper particularly cheered at the Ryouko (in a school uniform, using her bare fists) vs Amanae (in an elegant skirt and heels, swinging a friggin' CHAIN) fight in the fifth and last volume of Spiral Alive.
When Eyes outsmarted Ryoko in a game of dodge ball. It would d take a long time to explain his strategy here. So see for yourself how awesome Eyes was in episode 15.
All you really need to know is, basically, he won a game of dodgeball in one move with "logic".
Eyes' awesomeness knows no boundaries. There was one time and a Hunter was going to kill him during a concert and Ayumu figured out it was a sniper attack, telling Eyes to delay the show by five minutes while he and Kousuke incapacitate the hunter. What does Eyes do? Start the show two minutes early with a performance involving a lot of candles around him. So the heat rising will distort the hunter's vision from sniping. This also serves as a distraction so Ayumu and Kousuke could attack the hunter easier.