The scene where Miyagi demonstrates the usefulness of Wax On, Wax Off. The expression of confusion on Daniel's face slowly transitioning first to shock then to enlightened awe as Miyagi throws blow after blow at him and he defends himself without even realizing he's doing it tells the entire story.
Ali punching Johnny for forcibly kissing her to spite a nearby Danny does feel a bit cathartic, considering the wedge it nearly puts the couple through.
The "You're the Best" sequence, where Daniel shows everyone, especially the Cobra Kais, that the former punching bag is now kicking ass.
The final fight scene. Under injuries that would put a lesser teenager down and out, Daniel returns to the mat and dances around on his injured leg to get two points on Johnny before the Cobra Kai gets one on him. Then, even after Johnny has viciously targeted his previous knee injury, he remains in the fight. And when Daniel executes a perfect Crane Kick and wins the tournament, it is one of the most triumphant moments in 80s film. Even the Memetic Mutation that has rendered it comical can't diminish its awesomeness.
Leading up to the above, Johnny calling out Krease on his cruel teaching methods. Even though his talking back leads to Krease breaking his 2nd place trophy and putting him in a choke hold, it says a lot about Johnny for him to realize he and the Kobra Kai have been studying under a bully.
Daniel breaking the sheets of ice in the second movie. Made all the more awesome when Mr. Miyagi comes in and it seems like he's going to bail Daniel out. He is told that the odds are 3 to 1 that Daniel can't do it... and promptly bets six hundred dollars that he can.
Also from the second film, Daniel and Miyagi saving a few villagers, Sato and the bell girl when the typhoon hits.
The final showdown between Daniel and Chozen. As Miyagi puts it: "This not tournament, this is real!" Daniel could have gotten killed and he knew it. He still didn't back out.
While the mysterious "drum technique" that Miyagi talks about in the second film is nothing more than a roundhouse punch done repeatedly, there is that moment during the showdown between Daniel and Chozen when Miyagi plays the drum that that he says is the "secret" of the technique - and EVERYONE watching the fight joins in with their own drums. When the music builds as Daniel finally gets the idea - at the least, it's Narm Charm.
Part of the "drum technique" is defense — redirecting an opponent's force past you, a great metaphor for Miyagi's view of karate and life. This relies on great timing, and when the technique is turned offensive, it's the timing that's important. Every time Chozen winds up to attack, Daniel's fist is right there, pummeling him before Chozen can strike. It's brutal, and shows why Miyagi calls it "last resort": use it only when need to brutally beat down your opponent, and Miyagi's whole ethos is "don't let things get that far in the first place."
Daniel ending his fight with Chozen, hand held up to deliver the final blow.