It's odd to think of Duck Dodgers having Crowning Moments of Awesome, given that he's often played up as The Load and utterly inept, with much of his success being the work of The Cadet, a fluke accident, or both. However, there are moments where Dodgers manages to do exactly what he set out to do. These are those moments.
In the very first episode, Dodgers successfully laid out a seemingly unlikely plan to save the Earth by cramming loads of potatoes into the gun ports of the Martian ship.
In "The Spy That Didn't Love Me", he successfully laid out explosive charges on a tower broadcasting a control signal to the Martian Centurions, allowing an effective revolt against Martian control.
In "Enemy Yours", Dodgers gets two.
First, at the opening of the episode, he deliberately and successfully pulls off a Big Damn Heroes moment by putting his ship between Commander X-2's and a damaged Protectorate medical supply ship.
At the end of the episode, having previously made a fool of himself, manages to rescue the Martian Queen and defeat the dreaded Doctor Woe while wearing something that greatly resembles Doctor Doom's armor and firing Eye Beams at his opponent. He even treats the Queen with gallant chivalry.
During the trials to see if he was fit to be the King of Mars, Dodgers wins all three challenges on his own.
In the first trial, he goes Guile Hero on his opponent in a moment that would have made Bugs Bunny proud.
In the second trial, he not only survives the Martian Desert, he does so while eating copious amounts of salty snacks without water, and is able to endure the ordeal better than X-2 because he's lived in Palm Springs.
In the third and final trial, he defeats the Sages of Mars in a game of Three Card Monte. Effortlessly.
Of course, not every moment of awesome belongs to Dodgers. The Eager Young Space Cadet definitely gets one for taking on the titular characters in "Big Bad Bug Mamas" with a Giant Robot.
Commander X-2 manages to get one on Dodgers, as well. When it looks like his hated foe is about to become his King and wed the Queen, he convinces Dodgers that the King's sole purpose is to run the non-existent methane farms of Uranus.
In "The Queen Is Wild", Duck Dodgers displays surprising prowess with a set of laser nunchuku, using them to carve a giant snow sculpture of himself without even looking. He also handily parries the Queen's attacks.
Say what you will about Dodger's self-serving avarice, but when the chips were down, he really came through for the Green Lantern Corps, providing and entrance for Kilowog, Katma Tui, and Ch'p, and then, even as he was being pressed by Sinestro, using his borrowed ring to revive the captured Green Lanterns.
In "Hooray for Hollywood Planet", Dodgers manages to tame a rampaging space dragon by treating it like an overgrown puppy.
So much of the Season 2 finale, "Of Course You Know This Means War and Peace pts. 1 & 2".
The Martian Queen gets one for taking out Dish, who was already shown to be a skilled fighter as well.