And that lucky shot? They got him only because he had slowed down to turn and make another passage.
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.
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 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.
Episode 23: The Yamato has just rammed Deslers Palace in an attempt to take him out. Desler simply starts his personal ship and flees to the giant mobile Space City in Orbit and proceeds to throw a chunk of it on the Yamato and the Gamillan Capital of Baleras. Okita's reaction: