Bigwig gets one when Woundwort, his mooks having failed getting into the Honeycomb, goes in to handle it himself. He is stopped by Bigwig, who not only has buried himself in the tunnel for a suprise attack, but also manages to hold him off. Yes, hold off the rabbit chief who's rumored to have taken on a Labrador. However, the book's true Moment of Awesome comes from Woundwort's reaction to the You Shall Not Pass: he imagines that there is someone who can outfight Bigwig yet to face. For reference, find something that would make Stalin pee himself...
Bigwig: My Chief Rabbit has told me to defend this run and until he says otherwise I shall stay here. Vervain: His Chief Rabbit?
It actually becomes the crowning moment for two characters, both Bigwig, who just beat the Big Bad, and Hazel, who Bigwig swears at the beginning he would never call Hazel Chief Rabbit.
In fact Bigwig does use the honorific suffix 'rah' to Hazel for the first time after the terrifying escape from Efrafa; 'I couldn't do it again, Hazel-rah.' Of course a page or two later he's back to his old self. 'Now I'm going to sleep and Frith help you if you say I'm not, Hazel.'
Also when Bigwig replies with a blunt "Silflay hraka"(translation: "Eat shit") when Woundwort tells him to get out of his way.
Mild Fridge Brilliance there as well, since he called Woundwort embleer rah. "Embleer" is defined early in the novel as "the scent of a fox." So — "stinking prince" or "rabbit chieftain with the scent of a predator"?
It also succeeds in completely freaking out the other enemy rabbits, who are terrified by the thought of a rabbit even stronger than Bigwig waiting for them. Of course, the chief is actually the unassuming limping rabbit whom Woundwort casually ignored earlier.
One mass awesome moment: The escape from Efrafa. Not just Blackberry's The Plan and Bigwig's bravery, carrying it out, but almost every one of the rabbits, from Silver down to Pipkin charge into Efrafa to help the escape.
"Your storm, Thlayli-rah. Use it."
Fiver gets his Crowning Moment in the siege on Watership too. When the Efrafans break through the ceiling into the Honeycomb, he's in such a deep trance they assume he's dead. But once Bigwig beats off General Woundwort (see above), Fiver gets up and, still in a trance and seeming to channel something beyond rabbits, foretells the death of the Efrafan troops. Woundwart is oddly spooked just looking at him and orders one of his soldiers to kill him. But when talking to Fiver, said soldier hallucinates (or maybe not), that Fiver's summoning up all the souls of the rabbits he's killed as an Efrafan officer and he is soon begging for mercy. Soon enough, after the gambit with the dog, the Efrafans who didn't escape surrender themselves to Fiver, leaving him somewhat perplexed when he comes out of his trance.
Even more notable, because rabbits can only count up to four. As a result, virtually countless troops surrender to the Waif Prophet.
Not to mention that he first sends several enemy running with the screaming willies by channeling Something from the Other Side to give Hazel a vision of how to save them.
Just the fact that Hazel was hit with a shotgun, survived, managed to hide himself, and then walked home. Of course, without Fiver he would have died; but give the Chief some credit where it's due!
Hazel's visionary speech to Woundwart before he attacks Watership Down is subtle, but definitely counts. His more obvious one comes a little later when he sets a gigantic dog on Woundwart.
As the author points out, Hazel manages to expose Woundwort as the vicious tyrant he is, rather than the visionary he claims to be.
In addition, the more obvious one brings also an awesome moment for Blackberry and Dandelion — particularly Dandelion:
He tore over the crest and down toward the cattle shed. When Hazel had told him what he was to do, it had seemed to him that his task would consist of leading the dog on and persuading it to follow him. Now he was running simply to save his life, and that at a speed he had never touched before, a speed he knew he could not keep up.
In actual fact Dandelion covered three hundred yards to the cattle shed in a good deal less than half a minute.
Hyzenthlay deserves almost as much credit as Bigwig for the escape from Efrafa; he organized it, but she was the one who made it happen.
Woundwort himself has a crowning moment with his cry of "Come back, you cowards! Dogs aren't dangerous!" with the later implication that he not only survived the encounter, but actually sent the dog home early.
Bigwig: "I told you once I was trying to impress you. I hope I have."
Woundwort: "And I told you that I would kill you myself!"
Don't forget that Woundwort managed to take over a warren in spite of wild rabbits' attitude towards hutch-raised rabbits. Woundwort, you Magnificent Bastard, I read your book!
Let's not forget when Hazel pushed Bigwig aside and went out to meet the Black Rabbit of Inle in his place. The Black Rabbit being basically Death incarnate, and a Trickster version at that - the only being besides Frith (God) to out-trick the rabbits' folk hero El-ahrairah. No, it wasn't the real Black Rabbit, but their folklore made it real enough for the moment.
Finally, it should be noted that all these characters are non-anthropomorphic rabbits, and still manage to be every bit as much badasses as pretty much everyone else in any other work who has achieved a Moment Of Awesome, if not more so.
Blackavar deserves props for willingly taking the brunt of the Council's anger, to protect his friends from being mutilated after their escape attempt.
One of the in-universe stories has an exceptional CMOA for El-ahrairah, the legendary chief rabbit. To save his people, he seeks out the Black Rabbit himself and begs to trade his death for the survival of his warren. The Black Rabbit refuses (in a speech that is itself a CMOA). So he seeks out the hiding place of one of the terrible diseases the Black Rabbit uses to do his work, deliberately exposes himself and prepares to drag his diseased, mutilated body back to the waking world in order to save his people by exposing their enemy to the disease. At which point the Black Rabbit recuses himself, and aids El-ahrairah's people after all. El-ahrairah is preserved from death by a mere technicality - otherwise this would be a DMOA instead.
The fact that in the movie, Hazel is the recipient of a vision-speech that was originally given to El-Ahrairah himself when he offers his life to Frith in exchange for letting his plan save the warren.
"Not a day goes by but a doe offers her life for her kittens, or some honest captain of Owsla his life for his Chief Rabbit. Sometimes the bargain is accepted, and sometimes it is not. But there is no bargain here; for what is, is what must be."
Crosses over with a Heartwarming moment and a (happy) Tear Jerker, but it's no less awesome. At the end of the book, Hazel and Fiver's adventures have been immortalized as that of El-ahrairah's and Rabscuttle's.
"All the world shall be your enemy, Prince With A Thousand Enemies, and if they catch you, they will kill you. But first they must catch you—digger, listener, runner, prince with the swift warning. Be cunning, and full of tricks, and your people will never be destroyed."