Ikki defeating Magaki, the leader of the Skull Saders in his debut fight as a storm rider is definitely one. He wasn't skilled enough to defeat him in a straight up wall ride race for the emblems, so he utilizes the speed mechanics use of weight in Air Treks to kick one of his Air Trecks up the wall. Not only does he get the emblems before Magaki, but he knocks him out in the process.
Ikki's crow avatar turning the tables against the bird that tried to chase him while Ikki has a meeting with his friends to form the team.
Kazu's badass boast after he laid the smackdown against his former seniors who were ex-East Side Gunz members when they offered him position as the next head of the ESG.
Fat, perverted loser Onigiri's first, and for a long time only, Crowning Moment of Awesome came when, during his fight with Ryo Mimasaka, he, while paralyzed by her abilities, gave her a speech so enlightening and inspirational, it liberated her mind and her true self was made apparent to her. As it turns out, she'd "Spent my entire life fooling myself into thinking I had fangs." She was so elated to feel as free as she did that she took all of her clothes off (he helped her work out her body issues, too) and started shouting to the heavens about "freedom." He did that just by talking to her for about one minute. He defeated his enemy with sincerity, turning the tide against Behemoth and scoring an essential win.
Then, much later, Nike hits Onigiri's Berserk Button. While Onigiri doesn't beat Nike, he puts up a good fight and never gives in.
In one chapter, Agito beats at least seven Storm Riders while handcuffed and wearing a humongous, frilly dress.
Ikki breaking the record for the Devil's 33 set by Sora, while wearing the training weights Rika saddled him with.
Kazu moves so fast everyone else, including two King Level riders, can't track him. What does he say? "Give me a second, I need to unlock my back wheels."
The Ikki vs Ringo fight. Before that, you always knew that Ringo was an extremely skilled rider, but you never see her actually fight anyone who required more than a single punch to defeat. Then, she cuts off the weights that Ikki had always worn (including during his battle with Behemoth and when he made the Devil's 33 jump), letting him run faster than he's ever run before. She then proceeds to outpace him and utterly curb-stomp him. And then, after he got the Wind Regalia and they shattered, releasing horrendous levels of force, she stopped it all with a single attack.
Kururu rebuilding Ikki's broken Air Treks in less than three seconds.
She does something similar later on when she dashes past a soldier wearing Powered Armor, literally taking it apart as she ran past him.
Kogarasumaru's fight with the White Wolf Clan is one long moment for the White Wolf Clan. They're a bunch of old guys (and Canon) who joined the A-T world to market the merchandise that would save their company by beating Kogarasumaru and getting them to use their equipment. They win the respect of one of their biggest business rivals and completely take Kogarasumaru, the big name in the A-T world and the main characters, apart.
Usually, a good signal that one is about to happen is when a character's “shadow shows up, especially if it has changed since the last time you saw it, signifying the Taking of Levels in Badass:
Buccha enhancing his legs, changing him from a Mighty Glacier to a Lightning Bruiser, accompanied by a more science-fictiony tank shadow than his usual one.
"I might just be an average person, but as I stood with geniuses like you and Agito...I realized something. Once I actually tried to catch up, I realized geniuses aren't that amazing!"
Kazu vs Nike. God that battle was intense, namely with Kazu going beyond his limits and opening the door that connects him to other roads to utilize their abilities.
Nike stands up after taking a hit that also trashed an aircraft carrier. Never mind the fact that he was in no condition to fight; he still got up with only one leg after taking that attack. This guy takes determinator to whole new levels.
Pretty much everyone coming together to help Ikki make the Storm Regalia the best it can be. To summarize, Nue hands over the Thunder Regalia after Ikki beats him. After Kazu wipes the floor with Nike, Agito, Simca, and Kazu hand over the Fang, Gem, and Flame Regalias respectively
Kilik neutralising the Brainwashed and Crazy Rika and thus undoing Sora's Batman Gambit centered on how Rika's pregnancy with Sora's own kid would keep people from attacking her and thus opposing him. And then, he takes the Sky Regalia and fires it at Sora.
Sora reveals during his battle with Ikki that during every single battle that he has every been in, he never had his A-Ts turned on. Meaning he didn't need their power to get that strong.
In return, Ikki shows just how much stronger he has gotten to the point that Sora fearfully acknowledges Ikki has surpassed him in that battle alone. Thus making him need to use his contingency plan that is meant to kill Rika and their child by overloading her Regalia. To answer that, Ikki shows that he knew Sora would do something along those lines and gave Ringo the Storm Regalia, to counter whatever plan he has. EVERYONE thought that Ikki had the Regalia on the entire time. Showing these two know how to play a mean game of Xanatos Speed Chess.
Also in that battle: Sora was using the Wind Regalia, which incorporated twenty other Regalias, making them far superior to all other A-Ts with the exception of the Sky and Storm Regalias. Ikki was wearing normal A-Ts and still beat him.