In episode 20, he manages to defeat the Monster of the Week who was stealing people's love in a awesome way. The way he walks into the battle only adds into awesomeness.
In episode 2, Ryu takes on a giant jet monster on foot, by himself, and wins. True, he did wound it with his jet earlier on, but its still damn impressive.
The dogfight between Ryu and the jet monster. When the monster snatches up Gai to have a hostage? Ryu quickly targets its arm and flies by it as it's firing everything it has at him, slicing into it's arm to make it drop Gai and send it crashing to the ground.
Episodes 4 and 5 are basically Kaori becoming awesome.
Episode 6: Ryu's grandmother forces Mirror Dimension to release his captured victims by jumping in front of his capture beam and using a mirror to deflect it into Maria, trapping her and forcing it to release everyone to let her out. The Jetman team are impressed.
In episode 9, Raita frees his childhood sweetheart from Fashion Dimension's spell, shocking Trans. When the team starts beating the monster down, Raita comes up late. Why? He was busy getting his usual giant rocks...four of them which he uses to pound the living heck out of the monster.
Radiguet: Tranza, Try calling out my name. Tranza: (Shouting in pain) R-Radiguet! Radiguet: What did you say?! (Stomps on him hard) Tranza, Try calling out my name! Tranza: R-Radiguet! Radiguet: What?! Just Radiguet?! (Intensifies the pain towards Tranza) Tranza: (Shouting in pain) Lord Radiguet!!! Radiguet: That's Right! (Pulls the sword out of Tranza's palm) I won't kill you. You will fear my name your whole life, while living among the humans!
Episode 43: After Vyram nearly killed her and the Jetman, Commander Aya pulls a Big Damn Heroes to save Ryu, Gai, Raita, and Ako while they were in the Jet Icarus while she is in the Jet Garuda. Aya defeats the Bio Drill Dimension all on her own in a Curbstomp Battle. Now this is why Aya should have been an official Sixth Ranger!
She was also the one who managed to get Ryu out of the Monster of the Week's spell that made him lazy in the aforementioned episode 11.
There's Episode 3 when she's giving most of the team Training from Hell and has them attack her, curbstomping all three. Yes, they're untrained, but they've also got superstrength while she's just a Badass Normal. Later, when Facet Dimension attacks her, she manages to save herself. By cutting it's tendril off.With a razor.