The conclusion of Sword of Shannara, where Shea uses the Sword to destroy the Warlock Lord. Made all the more awesome by the revelation of what the Sword's power is, and Shea's stunned reaction.
In Elfstones Of Shannara Elven Hunter Crispin gets a Dying Moment of Awesome that counts here as well. After seeing his entire team butchered by The Reaper, he steps out onto a bridge to confront it, knowing full well that he will die in the process. He succeeds in his mission though: the kids he was trying to protect destroy the bridge, saving themselves from The Reaper.
Elfstones also features Allanon's aerial duel with The Dagda Mor, eighty-year old Eventine Elessedil killing The Changeling while injured and alone, and Wil Ohmsford overcoming the doubts that have haunted him for the entire novel, and finally burning The Reaper to ash.
From the climax of, Wishsong:
Brin, to the Ildatch after she's destroyed it: "Here is your dark child."
Also from Wishsong: Garet Jax, the Weapons Master, killing a Kraken with a harpoon. By jumping into the water with it and skewering it to death. And subsequently dueling against a Jachyra, a near unstoppable, demonic Combat Sadomasochist.
Free-born leader Padishar Creel gets one in Scions, when he lowers himself over the side of The Jut and uses casks of oil to send a Creeper plunging off the cliffs. He tops this a few days later when the Creeper returns and he tricks it into impaling itself on a giant crossbow bolt.
Wren Ohmsford/Elessedil's final battle against the Wisteron, where, like Wil Ohmsford before her, she manages to overcome her fear of the Elfstones, her doubts about her new role in life, all the trauma she's been through on the island, and her fear of the monster, and summon up the will to kill it. Doubles as a CMOA for the Wisteron itself, which shrugs off the attack that killed The Reaper, and forces Wren to bury it alive in order to stop it.
The conclusion, when Walker Boh, Morgan Leah, Matty Roh, Damson Reah, Coll Ohmsford, and Rumour storm Southwatch, free Par Ohmsford, and take down Rimmer Dall and his Shadowen. Individual Moments of Awesome abound—Coll gets his when he uses The Sword of Shannara to free Par from the Wishsong's control and Rimmer Dall's lies, Walker Boh gets his when he takes on Rimmer Dall mano-a-mano and fights him to a draw (and later interrupts his attempted possession of Par), and Par finally gets his when he uses his own magic and The Sword to free the bound earth magic imprisoned in Southwatch, taking down Rimmer Dall, Southwatch itself, and every Shadowen across The Four Lands.
Ahren Elessedil spends the entire trilogy being slowly transformed into The Woobie. Most of this comes at the hands of The Dragon, Cree Bega, a thoroughly repulsive Smug Snake. Then, at the climax of book three, Ahren finds himself trapped on a ship, alone, with Bega. And what does he do? He kills the SOB in an epic Knife Fight that probably ranks among the best in the series. Cree Bega himself gets a Crowning Moment of Evil a few seconds later: as he dies, he gives Ahren a glare so hostile that it nearly gives the kid a heart attack.
The final duel between Grianne Ohmsford and The Morgawr ends up being one for Grianne, her brother Bek, and believe it or not, The Morgawr. Grianne gets hers when she finally stands up to The Morgawr, calls him out on his evil, and concludes her trip to redemption by trying to rid the world of him, declaring her intent to become The Atoner. Bek gets his when, realising Grianne cannot defeat The Morgawr unaided, he uses his illusion powers to convince the Spirit of Mephitic Castle that The Morgawr is Bek, who stole one of its treasures in a previous book. And The Morgawr gets his when he not only overpowers Grianne during their duel, but when assailed from all sides by Grianne, Bek, and Spirit of Mephitic Castle, he briefly holds his own, keeping all of their magics at bay, and destroying much of the castle, before grudgingly succumbing.
For a moment he held them at bay, girl and spirit both, his dark heart long since turned to stone, his mind to iron. He would not be beaten by such as these, the bright glare of his green eyes seemed to say. Not on this day.
The Witch-Wraith/Grianne Ohmsford killing Tael Riverine in a duel for leadership over the Demonic hordes. After watching Tael walk away at the conclusion of High Druid, and kill Khyber Elessedil in Bloodfire Quest, seeing him finally humiliated and forced to pay for what he's done is supremely satisfying.
Paladins of Shannara
The short story The Weapon Master's Choice, adds a whole new CMOA for Ensemble Darkhorse Garet Jax (mentioned above under Wishsong, when he takes on a contract to save a colony of lepers from a dracul warlock. The story ends with Jax taking out a small army of mercenaries, and their vampire overlord, all with minimal assistance from the girl who hired him.