In what is generally considered the entire series' greatest CMOA ever, Dessler, the original Big Bad of the series decides to... pull a Heel–Face Turn and spare Kodai after Yuki tends to him. He spent the whole second series stalking the Yamato for payback and finally decides to make peace with his old enemies. From that point on, Dessler was the Earth's most reliable ally.
In the third series Dessler has one when he's told the ship that was giving trouble to his forces and had just been captured was the Yamato: without even raising his voice, his Death Glare and the 'disappointment' at some of his best subordinates forgetting the direct and explicit order to stay away from Earth and its ships nearly caused a mass heart attack.
The Yamato against the Dessler Mines (Dessler didn't name them): the Yamato was surrounded and couldn't escape, and the mines slowly moved toward her due the control signal. How did they survive that? Analyzer, while simulating the effects of drunkenness, found the control mine and deactivated it, stopping the approach of the other mines, and then the crew broke out the jetpacks and manually removed the mines. Dessler himself acknowledged this moment of awesomeness, and sent Okita a message congratulating him for this victory.
From the second season, the battle of wits between Kodai, who stole the Yamato to investigate what would be discovered to be the Comet Empire, and Ryu Hijikata (Draco Gideon in Star Blazers), commanding the super battleship Andromeda and with orders to stop the Yamato. Between Hijikata neutralizing all the attempts of evading him (particularly awesome and funny when it came to the Asteroid Thicket: the Yamato could fly at full speed through the asteroid belt thanks to Shima's skills, the Andromeda's computer couldn't fly the ship through the belt... so Gideon had his ship fly around the belt and wait for the Yamato on the other side), and Kodai's sheer confidence and courage, it was a true example of Cool vs. Awesome.
Deslar revealing he was still alive to the Yamato crew. Why? Because it caused the crew a mass Oh, Crap! moment and made them realize they could fail, whereas until that moment they were pretty confident they could win against the Comet Empire (especially after Sanada's latest trick), which was technologically superior to Gamilas.
In episode 18 of 2199, the Yamato bum rushing a Gamilas fleet of over ten thousand ships and managing to complete its objective while hardly taking a single scratch and while sinking multiple Gamilas ships (and a planet!).
The Battle of the Rainbow Cluster.
A Moment of Awesome in the second movie, Farewell to Space Battleship Yamato; not in a specific action, but by its pure inspiration. After watching the entire, built in the last 2 years, Earth Defense space navy get devastated on live TV, the alien Comet Empire demands Earth's surrender. Just before the surrender, the Yamato warps in between the Empire and Earth, and everyone on the planet says "It's Yamato! We still have the Yamato! We're gonna win!". Keep in mind we're talking about a SINGLE SHIP apprearing as a reinforcement after an entire FLEET was almost effortlessly destroyed by the enemy.
We would be remiss if we did not mention the Moment of Awesome in Final Yamato. The earth fleet has been wiped out and the planet Aquarius is on a direct collision course with our home. The only thing that can stop this disaster is the power of the Wave Motion Gun, set to a wide angle dispersal. The Yamato has been filled with a volatile explosive and gets underway to get into position to fire the gun and stop Aquarius — but the enemy fleet (with a vested interest in destroying Earth) moves to stop the Star Force. They can't fight back — the Wave Motion Gun is off line. They can't warp — there's not enough time. If the enemy engages the Argo, there's a good chance the ship will be destroyed before it ever reaches its target! As the enemy fleet prepares to fire, suddenly the flag ship explodes as Dessler and a Gamilas fleet (who haven't been seen all movie up 'till then) come charging in for the rescue. The Yamato's one time mortal enemy does a complete Heel–Face Turn and saves the day!