Almost everything Hayato does in the race track, but especially when he wins his first championship at the end of the TV series. After suffering multiple hardships (struggling at the beginning of the race, learning about his father's death etc), he finally earned his first championship win at the age of 14.
Hayato using his Internal Drift and Lifting Turn techniques for the first time, in Double-One and SAGA, respectively.
The final episode of SIN has Bleed Kaga's final race with Hayato. Kaga wanted to retire from Cyber Formula after the Japan race, but not before he beats Hayato once and for all. So in the last minutes of the race, Kaga used his boost from his car, Ogre, to defeat Hayato and manage to win the race and secure his first and only championship.
In EP 33 of the TV series, Randoll and Hayato used their boosts in the 8th race in Spain to go through the waves of the ocean before the waves crashed down on them.
Episode 32 the TV series also doubles as a heartwarming moment: Shinjyo's Fire Superion's engine went down as he was about to cross the finish line at the near end of the African Grand Prix. So what does he do? He pushes the car to the finish line and he managed to win fifth place in the race.
In Zero, he gets another one when he calls out Gudelhian after they have an argument when Gudelhian and the other racers trying to make a false report to the bosses that Hayato was driving recklessly (it's all Henri's fault), Gudelhian punches him, and in response, he gives him a punch that knocks him to the ground.
Miki gives Shinjyo a piece of her mind twice after he talks down to his newly-hired staff and lashing out at them for his poor performance in races, which made him realize that his problems are really his own doing. This event marks Shinjyo's transition from a full-blown Jerkass to being a much better person.