And right before his sacrifice, Mamoru gets one by bushwhacking a destroyer making a run at Okita's ship, scoring the only confirmed onscreen kill for the humans of the entire battle.
And that lucky shot? They got him only because he had slowed down to turn and make another passage.
The Gamilans being sore losers, they one-up him in episode 11, when Domel's fleet perform a very similar manouver with an entire naval division of destroyers, heavy cruisers, high speed cruisers and at least one battlecruiser. Needless to say, the poor enemy, a fleet of the Comet Empire, gets annihilated.
The Yamato gets jumped by Domel's whole fleet and has to fight its way out. On their route lies Domel's Dreadnought Flagship. Already damaged and low on power, they can't penetrate its armor on normal ranges. They then proceed to ram it, scrape alongside its length, blasting all the while point black with one of the main gun towers. From the look in his face, even Domel considered this as awesome.
Also, Domel being there at all. First, he had his men torment the Yamato for a while until she reached a certain place, then forced them to go at warp and, knowing that the Yamato could emerge only in one of five places due a pulsar, he guarded all of them, and as soon as she was in one of five places he had the rest of his ships move in for the kill. Had he been dealing with a lesser enemy, he would have won then and there, and with ease. Even then, he was still about winning (after admitting that the Yamato is a Worthy Opponent, even before the ramming attack), but he was recalled just as he prepared to unleash the coup de grace.
The Yamato surviving episode 8. Before them lies a star, behind them, courtesy of Deslar, there's a gaseous thing that will absorb the Yamato if it touches her and Shultz with his battleship (both to deliver Deslar's gift and to make sure the Yamato can't escape), and everywhere else there's an artificial sunstorm that will destroy the ship if they go anywhere else. How do they survive? Easy: flying near the star, to the point of grazing the corona. Thus, the star absorbs the gaseous thing and kills Shultz when he tries to finish the Yamato, and they survive the star's corona by shooting at it with the Wave Motion Gun, thus opening a path in the same plasma tendril that destroyed Shultz's ship. By surviving all of that (and a trap organized by Deslar himself), the Yamato got promoted from "plaything" (in fact Deslar was treating Shultz's transmission as an entertainment) to Worthy Opponent. And got Domel sicked on them.
At the end of episode 16, Yuki, Kodai, Shima and Hoshina are fighting the mutinied security, but even with Itou disarmed and Niimi unwilling to go over the Moral Event Horizon they're outnumbered and outgunned. Things look bleak... Then Okita shows up and calls Itou an idiot, and the mutiny ends that very moment.
Episode 19 has not been released yet as this is written, but the next episode trailer for it shows that Domel and the Yamato crew will still have their ultimate Crowning Moment of Awesome the attack of the teleporting starfighters that nearly destroys the Yamato, and the crew not only surviving but annihilating his carriers.
Episode 19 confirms it, showing the preparations of Domel's task force composed by his flagship fitted with the teleporters and four carriers crewed by young recruits and recalled veterans, plus a group of volunteers from Zalts with a special task: board the Yamato with Frakken's help and kidnap Yurisha.
In the same episode, the Yamato has to choose between passing through the navigational hazards of the Rainbow Cluster or travel around it. Okita decides to pass through it to spare time, reasoning the enemy wouldn't expect something that crazy and keeping the ship at full alert in case the enemy actually ambushes them there (what he expects to happen if the Gamilas commander of the ambush near the neutron star managed to get back). Domel goes there to wait for him, because Okita is the kind of man he thinks he is, and is the Gamilas commander of that ambush.
Episode 20 finally has the Battle of the Rainbow Cluster. The awesomeness defies words, so we'll just say the result: after the toughest battle in the series, the Yamato destroys the carrier and survives Domel's final Suicide Attack, but the commandos have kidnapped Yuki (who they believed being Yurisha) and delivered her to Wolf Frakken, who escapes with the prize. That, and one single moment: one of the old veterans, discharged due old age before being recalled, muzzled the Wave Motion Gun and nearly destroyed the ship with a repurposed drill for asteroid mining, only for Niimi and Analyzer to commandeer it and use it to destroy two carriers, including the one that had launched the bomber that fired the drill. The only reason this is not spoilered is that it comes straight from the original series, so you should already know of it...
The muzzling of the Wave Motion Gun is such an epic moment that, in spite of the many changes, the movie had it too.
Some more awesomeness for the staff, for making the awesome moment of the original series even more awesome.
Episode 17 has an Heroic Sacrifice for Sanada: to activate the portal that will allow the Yamato to skip 30,000 light years, he needs to stay in a control room that will be saturated with neutrons, killing him... And he does just that. More awesomeness ensues when Sanada subverts it: there was a pool in the room, and, knowing that neutrons have poor penetration in water, dove into it before the room was saturated.
After which he takes on twenty-eight ships and win.
But before that we had Goer's awesomeness, for pulling a manouver worth of Domel: he managed to sneak up on the Yamato with thirty ships. Had he been there to destroy it instead of sending her into Dessler's ambush, he would have succeeded. That, and Frakken's intervention didn't prevent him from doing his part in Dessler's plan.
Oh and he nearly killed Frakken: his squadron had hit the subdimensional engines of the submarine, and without an emergency repair (performed by former Yamato crewmember Yabu, of all people, they would have remained exposed to the enemy fire.
The Yamato versus Wolf Frakken's space submarine in episode 13.
Zoellik's Humiliation Conga in episode 18 is one for everyone involved in delivering. In order, the Yamato interrupts his Rousing Speech to the ten thousand ship that he was trying to have as support for his coup, then in the battle he ruins his image before supposed The Dragon Goer and the fleet, and when the Yamato appears to have been destroyed Deslar reveals he survived his apparent assassination and reveals the culprit was Zoellik himself, at which point Goer gets fed up with him and shoots Zoellik in the back with his own gun. And finally, to ruin even the possible glory of taking down the undefeatable battleship that not even Domel had been able to destroy, the Yamato re-emerges from Balan's atmosphere (where they had hid) and wrecks the planet and the Gamilas' Portal Network with the Wave Motion Gun.
This is one especially for the Yamato, that has just taken on ten thousand warships and won. And left the bulk of Gamilas' fleet unable to give chase. Of course, that gets Domel sicked back on them with orders to destroy the Yamato or die trying...
Then Deitz (who had been imprisoned on the planet after being framed for treason, hence Melda starting the riot in the first place: it was supposed to be a distraction while she sprung him out) does his thing, and enrolls guards and rioters in his revolution against Desslar. Remember, the Gatlantideans are war prisoners who have joined the commander of the guy who defeated and captured them and killed their friends...
Episode 22 ends with the start of the Battle for Iskandar. Dessler's opening shot? The Dessler Cannon.
After the Colony Drop failed, Dessler tries again with the Dessler Cannon. Due to Yuki and Nolan's sabotage, it blows up on his face, with the explosion wiping out the space city and the Imperial Guard.
The Yamato's first fight with Goran "Thunder" Dagam and his Gatlantean fleet, whose flagship Megaluda carries a Magna Fire Cannon. The Gatlantean are sure to win... And not only the conventional methods are ineffective, but the Yamatosurvives a shot from the Magna Fire Cannon, even if with drained shields.
Knowing they would not survive a second shot, the Yamato goes in a nearby cave planet, only to be assaulted by energy-draining lifeforms that are immune to normal weapons. How does the Yamato survive? Warping out at low energy.
Kodai's scout group and Berger not trying to kill each other in the face of Lorelei using her vast psychic powers to manipulate them into that. Made more notable because Berger has a personal vendetta against the crew of the Yamato and Lorelei managed to get a group of Gatlanteans from the same unit to kill each other.
The Yamato and a Gamilas squadron fighting together against Goran's fleet. Made even more awesome because the Gamilans are survivors of the Rainbow Cluster: it's literally Domel's men fighting alongside the Yamato against Domel's great enemy.
The Gatlantean squadron has the Magna Fire Cannon, that uses Gamilan teleporter technology to attack from beyond the range of enemy weapons. Thing is, it's the same technology that Domel used at the Rainbow Cluster... And with this, the Yamato can anticipate the incoming attack and tell everyone when to dodge.
Note that the Yamato fought this battle without the Wave Motion Gun, as Starsha muzzled it when she gave Earth the Cosmo Reverser. Some doubted of their ability to pull it off if attacked... And yet, they were barely slowed down.