Artemis and Butler manage to have these moments en masse, though Foaly isn't too far behind either.
Artemis Fowl (The Book)
Butler wanders unarmed into the middle of a heavily armed and invisible group of LEP commandos, and proceeds to wipe the floor with them.
Shortly after the above, Butler trumps that by taking on a troll (which in the Artemis Fowl series, are 10 foot tall, 900 pound, crazed engines of death, with retractable claws, and poison tusks) and beats it to a quivering pulp, using a mace, ancient knight armor, and his BARE HANDS. Once Butler's done beating the troll to a bloody pulp, he proceeds to forcibly chuck the broken 900 pound killing machine out the front door, while nonchalantly stating: "And don't come back."
Even the human-hating fairies acknowledge it as awesome (it basically turns Butler into a legend, with the footage of the battle used in LEP training videos), and one of them has to be assured that it wasn't a hallucination brought on by delirium from severe wounds. Holly's encounter with the troll in Italy that's used as a bad example is in the same one as this moment. Butler's confrontation with the same troll is far too Badass for the fairies to receive it negatively. Holly's is used by her instructor in a class she takes. Butler's is in the hand-to-hand combat instruction class.
Artemis's and Root's first "meeting" on the booby trapped whaling vessel, Root is smug until he sees the LCD countdown and Semtex.....
Artemis, at age 12, managed to translate the Fairy Booke over 18 hours, the first human in a thousand or so years to achieve this feat.
Artemis escaping the bio bomb with sleeping medicine.
The Arctic Incident
Butler takes on about 200 heavily-armed goblins, with nothing but a SIG pistol and his fists. He gets through about 50 of them, before the rest flee in terror from the terrifying god-mountain. As the book puts it "There were only two people on Earth more well-versed in the martial arts than Butler. One was related to him. The other spent his days alone on a small Pacific island, meditating and beating up palm trees. You really had to feel sorry for those goblins". To give you an idea of what exactly that entails, he is described as "a ton of bricks, but with considerably more economy of movement."
In the graphic novel, one panel shows Butler out of ammo and surrounded by goblins. The next few panels show what else is going on, and then it cuts back to Butler, who is still surrounded by goblins, all of whom are unconscious. He took them all down offscreen.
"Two hundred goblins versus two LEP officers, one human and one working weapon. This was going to be close."
Holly during the scene with Root, the ship, and Koboi Labs. "Let me ask you something. How fond are you of your ribs?"
Holly having her Awesomeness by Analysis moment in the Arctic and using a nuclear-waste transporting train to free Commander Root and Butler from under tons of ice and snow, coming up with the plan in moments without Artemis's help.
The climax is a brilliant CMOA for Foaly. Basically, he uses his tech genius and some secret footage of his conversation with one of the villains to turn the joint Big Bads' army against them, and then the Big Bads against each other. All from inside a locked cell. It's probably the only adventure in which Artemis relies entirely on someone else's plan to save the day.
Even better? Opal never realizes that the breakdown used to cover this action up was faked. She honestly has no idea just how badly she was Out-Gambitted.
Artemis then gets one when he rescues his father by having Butler shoot him with a sniper rifle loaded with a well-placed Chekhov's Gun.
Trouble Kelp's defense of Police Plaza. Managing to keep the enemy off without working weapons until the heroes could win the day. Bad. Ass.
The Eternity Code
In the beginning, Holly yells at Artemis for putting fairy technology in Jon Spiro's reach.
Holly: You gave fairy technology to a man like Jon Spiro? Artemis: I quite obviously didn't give it to him. He took it. Holly: Don't play the victim, Artemis. It doesn't suit you. What did you think? That Jon Spiro was going to walk away from technology that would've made him the richest man on the face of the planet?
Juliet manages to infiltrate a SWAT Unit and convince them she's a rookie. All after she convinced a desk clerk at the building the rest of the crew were infiltrating that she was a little girl asking if her "invisible friend" could come along (so that Holly could enter the building - Fairies have to have permission to enter a human dwelling in order to enter it without becoming sick)? Cute, powerful, and versatile.
This troper can't believe an earlier scene in the book, where she first confuses two muscle bound henchmen with what can only be described as Psychology Babble, then completely mops the floor with them.
"Guess what?" "What?" said Pex. "You're not supposed to deep-fry sushi."
Butler throws himself in front of a bullet meant for Artemis, and then (even though the bullet went through his heart) he manages to remain conscious long enough to shoot the would be assassin in the head. It should also be noted that he was essentially blind when he made that shot. When this fails to kill him, Butler later returns (his heart got better) and manages to convince the hitman that he is a spectre sent from hell to claim him, which leaves the hitman a gibbering wreck, promising to confess to every crime he's ever committed.
Arno Blunt breaking out of a guarded police van. On his own.
Mulch climbs up a freaking skyscraper barehanded. While Juliet is tied to him.
Artemis outsmarting Spiro in the end. Artemis planned for Spiro to prevent him from recovering the cube, and had Holly plant a hypnotic suggestion into two of Spiro's goons, causing them to suggest Spiro break into a rival company's HQ using the cube. He takes Artemis along as insurance, only to find himself trapped inside as a SWAT team kicks the door down and Artemis vanishes, using the cube to erase all evidence he was ever involved.
All the better to see you with, Spiro.
And as an addendum to that:
Artemis: (to Spiro) About my name- Artemis- you were right. In London, it is generally a female name, after the Greek goddess of archery. But every now and then a male comes along with such a talent for hunting that he earns the right to use the name. I am that male. Artemis the Hunter. I hunted you.
The Opal Deception
Root's horrible replacement, Sool, has just given the order to blow Holly's shuttle out of the air - the justification being that she supposedly killed the Commander). Foaly is arguing with Sool in Trouble's earpiece. Trouble and Holly were friends, but he doesn't have any of the proof about her innocence. So he fires... a comlink.
Holly making it to Munich to save Butler and Artemis under Root's final orders, which she swears to follow to the letter, and managing to defeat Opal and bring back Artemis's memories.
Holly pilots a shuttle without the engine to hide their heat signiture from heat seeking missles. Yes, being an ace pilot is a necessary plot skill.
Of course, Opal's escape plan deserves mention. She broke out of jail in such a way that no one would even realize she was gone until she revealed herself. This then rolled right into her revenge plan, where she frames Holly for Root's murder, and makes it so that even if Holly escapes, no one will believe her claim that Opal escaped.
Holly and Artemis hold off a bunch of trolls with only their wits and a pair of fairy handcuffs.
Artemis's final gambit against Opal: He has Mulch break into her shuttle and steal her two bombs. When Opal discovers this, she attempts to kill Artemis & Co by detonating the bombs remotely, but cannot. They then taunt her with the fact that they have also stolen her chocolate truffles, tricking Opal into opening her x-ray proof safe and allowing the bombs to arm... while they're still on Opal's own ship. Cue the best Oh Crap moment of the series.
The Lost Colony
When Artemis figures out, in his head, the pattern in which a dimension is fading from time and space and uses it to save Holly's life, in the past, from the future.
Minerva gets one where she's able to kidnap N°1 and whisk him away before Holly can do anything. Artemis knows this, doesn't bother to do anything and afterwards, applauded her.
The Hostage exchange on Taipei 101, Artemis is able to pull off a gigantic Batman Gambit, save Minerva, extract N°1 and initially get cleanly away from Billy Kong's Hit squad. On a side note, he also subtlety manipulated Kong into choosing the meeting spot where he would have the advantage.
Butler holding a trained killer with deadly martial arts to the wall, then throwing him across the room for Holly to shoot in mid-flight.
Early in the book, Butler literally pulls Artemis out of the past.
The Time Paradox
A tie in to the original. Ten-year-old Artemis wakes up after the events of The Time Paradox saying "Fairies. Something about fairies."
Holly scares off a fully grown silverback gorilla while in the middle of his territory that's just horrifically injured Artemis. She then proceeds to heal him, kiss him and get them the hell out of there.
Artemis beating the Extinctionists at their own game in the courtroom scene, fighting for Holly's survival.
The Showdown with Opal Koboi on the giant steps, starting with a horse chase, turning into a aerial chase and finally an epic standoff where Artemis instigates another Batman Gambit which ends up destroying most of the giant steps and burries Koboi alive.
The Atlantis Complex
When Artemis knows that once Turnball gives him an order he will be unable to disobey, so he goads Ragby into shocking him, knowing this will trigger the complex and bring the Orion personality - which is not under Turnball's control - to the fore. He finds a way to use a serious mental illness to defeat the Big Bad.
Leonor Carsby wrestles free from her husband's influence, tells him she's ready to die and gets to fly one more time as she pilots an ambulance into the Atlantis Trench to save an underwater hospital.
The Last Guardian
The climax of The Last Guardian: Artemis, with an unconscious Holly in tow, appears to surrender to Opal as she is about to unlock the second seal on the Berserker Gate. Not willing to pass up a chance to gloat, Opal indulges herself and gives a typical villainous lecture. Artemis argues and states he could make a plan using Holly's magic to stop the spell. Opal mocks Artemis by waving Holly's hand over the magical off-button of the lock, stating that the seal can only be broken by Opal only due to DNA coding. Turns out Holly isn't actually Holly, and Opal just placed her clone's hand (from book 4) to dispel the gate. Artemis manages to pull off the ultimate Batman Gambit with nothing else left in his arsenal. This also gives big props to Nopal, who managed to derail the final evil plan of the series and save the world while appearing in a grand total of four scenes in two of the eight books and not speaking a single line of dialogue.
Not forgetting what happens after that: The gate being dispelled means that a magical corona will trap every fairy in there and take their soul to the afterlife. As Artemis has a fairy eye, this includes him, leaving his physical body dead. However, through a combination of his humanity and sheer willpower, his spirit manages to remain on Earth, and he arranges for Foaly to make a clone through a DNA sample he'd left on Holly by kissing her. His spirit merges with the clone, meaning Artemis has come back from the dead. An Ironic Echo, considering Opal earlier mentioned to herself that even Fowl couldn't do that.
Mulch takes control of a freakin' troll and rides it to rescue Holly and Artemis.
Engineer Kolin Ozkopy is a two-shot character who at first seems to be merely the victim of a horrible Punny Name. That is until he stares down a super-charged Opal, realizes she is about to kill him and manages to mock her badly enough that she remembers it for the rest of her life.
Beckett Fowl punched Opal while being possessed by one of her minions.
Artemis informs the group that to destroy the Berserker Gate they will need a super-laser. One of which he has in his barn. No one else is surprised to hear this, though Butler is quite annoyed that Artemis built it when he was supposed to be exercising.