The very first episode has all of the girls performing a Big Damn Heroes moment when they use Washu's teleporter device to see Tenchi... just as he and his grandfather are about to be killed by a bunch of evil spirits. Ryoko, Ayeka, everyone sports a menacing Death Glare right before they destroy the poor bastards for trying to hurt Tenchi.
Ryoko: You little twerp. I am Ryoko! And I am not one to be trifled with!
Episode 19, when all of the girls are driven away one-by-one as Yugi's schemes give fruit and Tenchi falls sincerely for Sakuya... Ayeka actually refuses to leave even after being given proof of Tenchi choosing Sakuya. Considering how much of a Clingy Jealous Girl she can be, the fact that she didn't fall for it is rather good. And then we see that Washuu didn't "leave" either. All the time she spent in her lab, apparently disconnected from everything (which would be her equivalent to "leaving")... she spent it researching and doing what she could to try finding WTF was Yugi planning.
Ayeka gains one early on, mixed with Heartwarming Moment. In her quest to go from Okayama to Tokyo (with Sasami and Ryo-Ohki in tow) in episode 14 "Tokyo or Bust", she befriends Masayo whose boyfriend Isao is away (though in reality they're falling stars given human forms, and she's forced to work for Yugi so she and Isao won't literally become Star-Crossed Lovers) and she's chasing after him. And once Ayeka learns that Masayo is a Heartbroken Badass and may not be able to see Isao again... she decides to forfeit the chance to go to Tokyo, and pours all of her (and her sister and Team Pet)'s efforts on reuniting Masayo and Isao. And it ultimately works.
Amagasaki practically gets a whole episode of Awesome (and Funny) in episode 15, "Love Match". When he repeatedly clashes with the spirit of a famous female Pro-Wrestler and finally defeats her.
Tsugaru's final fight against Mihoshi and Kiyone in episode 25. Basically, Mihoshi and Kiyone's normal blasters have no effect on Tsugaru, Tsugaru is eventually killed when he's shot with a gun loaded with an anti-matter bullet that totally vaporized him! Made even more awesome because this is a CMOA for... Mihoshi. Yes, Mihoshi. Had she not taken the bullet for Kiyone instead of shooting Tsugaru with the anti-matter bullet, Kiyone would have not had the chance to catch Tsugaru with his guard down enough to kill him.
Sakuya gains what might be the biggest CMOA in the whole series. Having been re-absorbed into Yugi, which would be the closest to death for her, she's put into a Lotus-Eater Machine with the intention of locking Tenchi inside of it forever as Yugi takes over the earth. Only that Sakuya, who by that point is far more than a mere projection, refuses to play along. She tears the LEM down, gives Tenchi a Rousing Speech, and sends him back to the girls, fully knowing that she will disappear out of existence.
Sakuya: I'm so happy, I've waited so long for this moment. But I'm afraid I have to go away now.
Tenchi: Sakuya?
Sakuya: I'll be alright. Of course, it's such a pity...but we've had a great time. To bad we can't just, dream on.
Yugi: (gets confused and angry at Sakuya's rebellious behavior) What are you trying to pull on me?! I don't need you anymore! Your finished!
Tenchi: Sakuya! Let me tell you...
Sakuya: No, you don't need to say anything. I know how you feel. But no matter how beautiful and joyful this may seem, it's only a dream world. And people can't live on illusions. Tenchi, you have an important mission to accomplish. People are depending on you. And your home is waiting for you. The time we've spent together, every smile, every touch. All the hopes and dreams we had for the future. I will cherish them all. I will treasure every memory. And my treasure will remain right here. (places a hand on Tenchi's heart) I have it all Tenchi. And I wont wonder about my past, and I wont feel lonely, ever again.
