Alanna's entire fight with Ralon in The First Adventure. He's bigger than her, and has been tormenting her for months, and yet she refuses any help from her friends and takes him on alone. And completely trounces him.
Also, her defeat of the Ysandir with Prince Jon.
"She had shown the Ysandir that a girl was the worst enemy they could ever face."
George Cooper. He's amazing with knives, incredibly intelligent, and the King of Thieves by the age of seventeen.
Alanna's duel against Dain of Melor. She's only a squire at the time and beats the snot out of him after her breaks the rules and tries to kill her. All with her less dominant hand. Which is related to another Moment of Awesome, namely learning to sword fight with her left hand and a too heavy sword after her right arm is broken.
At the end of the second book, Alanna publicly accuses Duke Roger of murder after uncovering (with the Chamber's help) evidence of his Evil Plan. She defeats him in single combat in front of the Court, in spite of the fact that she's only just been knighted and he is a veteran Magic Knight.
The climax of Lioness Rampant. Pure chaos as the various evil plans all come crashing together, and just about every named character gets something big to do.
Alanna spends her quartet gathering powerful friends and cool artifacts, but the climax of the fourth book means losing, sacrificing, or leaving behind each and every one of them as she descends into the catacombs under the palace to face Duke Roger.
The Immortals
Angry Daine unleashing skeleton zombie dinosaurs = the series' most visually spectacular Crowning Moment.
Also, her final showdown with Ozorne in "Realms of the Gods", where she spends the entire fight dodging every piece of magic the Stormwing throws at her by constantly shape shifting, and when she has no magic left, stabbing him in the chest with her badger claw.
On a related note, Numair turning a man into a tree. And just to be safe, making a tree (some tree, somewhere) into a person so the universe it balanced.
The attack on the hydra monster in The Realms of the Gods, including the Badger chewing through a skull to the brain, and a flock of starlings mobbing it.
Daine is instinctively reluctant to accept the kraken's offer to help defend Pirates' Swoop. We immediately see it justified: it reaches them from deep beneath the waters of the Copper Isles three days away by ship within hours if not minutes, then completely tears apart the attacking ships that even an adolescent dragon couldn't take on.
It's either another moment of awesome for the kraken for requiring the combined might of the most powerful mage and the greatest knight in Tortall to be driven back, or for Numair and Alanna for being able to drive back such a powerful immortal. Or both. Both is good.
Protector Of The Small
Lady Ilane of Mindelan once gutted a bunch of pirates that were trying to steal holy artifacts from a Yamani shrine, an act that lead almost directly to Yaman wanting to ally with Tortall. It was also one of the things that inspired her daughter Keladry to train for knighthood.
Kel's explanation for why she's all but declaring war on hazing, and her friend's response to it.
Kel: "If we take this as pages, what about when we are knights? Do we say, Oh, now I'm going to be nice to the weak and the small? Or do we do as we learned when we were pages? I don't mean to lecture. You can laugh and say I'm a silly girl - but when I see anyone big pick on someone small, well, there's going to be a fight. Joren and his friends are out there looking for someone to hurt. I want to stop them."
Neal: [...] "You're the oldest ten-year-old I've ever met. [...] It means I'm trying to justify to myself the fact that the best lesson I ever had on chivalry came from someone five years younger than me. When you put it that way, well, I guess I'd better help."
Kel takes her Bully Hunter tendencies to their natural extreme in Squire, fixing the Chamber of the Ordeal itself with a brutal "The Reason You Suck" Speech for its brand of testing—after seeing the way it broke true monsters like Vinson and Joren, she'd expected existential tests, devastating moral and ethical quandaries, great and terrible visions that would strike at the heart of what it meant to be a knight—and received, instead, "merely" being forced to face her own worst phobias.
Kel: This is just mean! You're a nightmare machine, bringing bad dreams to people who want to help others!
This becomes a CMOF when you consider that one of those phobias is in fact an appropriately existential lesson about properly valuing her own skills as a commander by showing what would have happened if she failed to develop them, but by that point Kel is too offended and furious to notice. Thankfully, as this is a case of genuine (if unexpected) moral outrage and not actual inflexibility or refusal to accept the lesson, and her rant is delivered without breaking the rule of silence, the Chamber approves rather than reject her for it.
A group of pages including Kel are sent to map an area and catch some game during summer training and find a camp of burly adult bandits. When the senior pages freeze up, Kel keeps her head and rallies her friends into a tactical retreat. One man on a horse charges at Kel as she brings up the rear. She guts him with a spear and continues to keep the group together while they reach a more defensible position until their training master arrives with The Cavalry. (Bonus points for the defensible position being on a cliff, which she leads them up despite still vomiting from heights). How old is she when she does this? Twelve.
At the end of Page, Kel chooses to climb Balor's Needle, a tower that she couldn't climb down from on a normal day until the King put her into a trance, to save Lalasa and Jump. Not only does she have to make the climb while making sure Lalasa doesn't panic, she also risks having to retake all four years as a page because she's missing the exams to become squire.
Kel's defiance of the Standard Female Grab Area in Squire. When Lerant insults her and grabs her arm, she simply flexes her bicep, which becomes so big that he can't keep a grip on it.
Kel spends her first year as a page enduring constant and vicious bullying. Soon, she figures out that someone weighted her lance with lead to make her look awkward. When it breaks, she gets handed another such lance by Joren. This is so unjust that Kel finally breaks...by going into Tranquil Fury so calm that nobody can tell, and then becoming the first trainee to hit the target. With her weighted lance. She goes on training with not only the weighted lance, but weighted axe and sword as well, becoming so used to them that when she breaks the second lance and finally gets a "normal" one, she has to take it to the palace carpenter to be weighted because the normal one is too light.
To add onto this? She keeps pushing herself until she can hit dead center every time, uses a willow ring (most rings are oak; the willow ring is much lighter and thus sways much more in the wind) to train with, and becomes the best in not only her class, but the entirety of the pages.
Lord Wyldon thinks women should Stay in the Kitchen (this attitude being a serious problem is underlined in Tortall: A Spy's Guide) but grudgingly, in spite of himself, he's repeatedly impressed by Kel and ashamed to realize that he barely listened to the voice of honor and gave her any fair treatment at all - he realizes that both in spite of and because of his efforts, Kel is the greatest knight he's ever trained, and steps down because he came so close to disallowing her from passing probation.
Every time Kel fights a killing device. She always finds it upsetting and frightening but of course that doesn't stop her.
In Squire it's a hard, brutal battle against a new, horrifying kind of monster and Kel manages to win thanks to a combination of her superior training and equipment, fast thinking, and leadership skills which enable the squad she's commanding to help her immobilize it so she can pierce its head with a warhammer.
The first time she encounters them in Lady Knight Kel is on a wall in a siege and hears screaming as a killing device crests the wall. She demands a crossbow and runs towards it. Her presence gives her people confidence that they can overcome the monsters.
On the road to Blayce's fortress tactics for facing killing devices have developed to the point where dispatching three is nearly casual, which is anticlimactic but does show that the Tortallans are smart.
Neal dealing with Tobe's abusive former master, by putting a spell on him that will make him feel every piece of physical abuse he gives out himself. Just to make sure the man understands that it's real, Neal says "Mithros cut me down if I lie."
Kel's "The Reason You Suck" Speech to Idrius Valestone, including turning his sexist rhetoric around on him by mocking his baldness.
Kel's mission to rescue the refugees who were kidnapped from Haven. Throughout the whole thing she proves herself an excellent tactician once again, whittling down the enemy's far superior numbers using every trick she's learned over the course of four books, before the final showdown with Stenmun and Blayce.
The refuge kids' use of the tricks Kel taught them to aggravate their captors and give their rescuers something to follow; Kel is beyond proud.
Kel in general as unlike the other heroines in the series, she doesn't have any form of magic and until Squire, didn't exactly have any kind of divine assistance or mission from the divine. She is pretty much the Badass Normal heroine of the series.
Kel is a blazing idealist who ardently believes in a form of chivalry in which the strong don't just protect the weak but help to lift them up without condescension. The world she lives in is imperfect - it's actually grayer and harsher than the previous two quartets had seemed - and she can't simply overcome systemic oppression, but her commitment to other people and her own code is so strong that it moves others to reconsider the status quo. Kel's speech in First Test ends with an Armor-Piercing Question about whether people who accepted cruel hazing as pages will really come to think that they should protect the weak and the small that persuades her friends to join her. Her support for Lalasa gives Lalasa strength and confidence that Lalasa carries forwards to teach to others. The Monarchs agree to change an unfair law. There's a real sense that Medieval Stasis is not enforced here, and Kel's example and influence are shifting things for the better.
Daughter Of The Lioness
The female Balitangs all get some good hits in during the final chapter of Trickster's Choice, with Sarai turning on Bronau once and for all, Winnamine killing one of his henchmen with a candelabra, and Dove getting rid of the bastard for good with the arrows Nawat gave her. And then there's Nawat pulling a Big Damn Heroes by convincing the other crows to take human form for a little while.
The raka citizenry rising to the defense of the Balitangs when the King's Watch tries to assassinate them. Centuries of oppression finally begin to be thrown off for good. And including the amazing image of two women, one raka and one luarin, working side by side to fight the soldiers, giving hope that there can be peace between the two sides after the rebellion ends.
The last bit of Ulasim's speech after the riot: "Any child knows it is better to swim with the tide than against it. We attack in force at dawn."
How Dove is so intelligent, and commands such respect, that she is able to make all the luarin nobles in the resistance, many of which are over twice her age and look down on her for her mixed race, listen to her and accept her as leader.
Dovasary Balitang, hope of a nation, future queen of the Copper Isles, spends the climactic battle of Trickster's Queen circling above Rajmuat astride a copper-colored kudarung — the winged horse that served for centuries as the symbol of the Haiming queens. It is the most unsubtle, in-your-face metaphor in the whole 'verse, and by all the gods, it works like nothing else.
Provost's Dog
When Goodwin is hit hard with a knife-hilt during a domestic dispute and goes down, Beka apprehends the woman who did it by jumping out a window after her and chasing her down a number of dark, twisty streets, all while the woman is hopped up on basically amphetamines. It thoroughly impresses everyone who hears about it, even when she's having an internal meltdown over recounting the story on Court Day.
The Growl in Terrier.
I'd heard of a Growl, when Dogs took up a challenge. It meant ill for the Rats that made them voice it. But it was one thing to hear of it, another thing to sit in the Mantel and Pullet and hear that rumbling snarl come from dozens of throats.
Beka, Achoo (and to a lesser, extent Goodwin) managing to chase Pearl for hours, until they're all weary and exhausted, but continue to fight, even when they're in a filthy sewer filling with water.
: the baby Thayet 'found' after attacking a band of army stragglers.