Haruyuki's second battle against Ash Roller, where he outsmarts his opponent by exploiting a critical weakness in his bike.
Haruyuki's first battle against Cyan Pile, where he unlocks the ability to fly, which is an ability that had never previously been seen in the Accelerated World and causes all of the spectators to shit their pants in surprise.
Scarlet Rain: You better remember this! This is a battle between two Level 9s!
The moment when Haruyuki equips Gale Thruster in episode 17. Pretty much the best way to equip stuff in games ever.
And then there's episode 22, where Haruyuki actually uses his detective skills to figure out how Noumi manages to stay off the matching list. Noumi's Villainous Breakdown when he finds out merely seals the deal.
Episode 23. To wit:
Taku's Incarnate System training with Niko really paid off, as Cyan Pile was able to turn his pile bunker into a freaking sword! At last, he's now a true blue Duel Avatar.
Haruyuki managed to will himself out of his own Heroic BSOD, and eventually Black Vice's supposedly nigh-inescapable Death Trap!
Episode 24! Chiyu outsmarts Noumi by reverting his avatar back to before he stole Haruyuki's wings, meaning Haruyuki gets them back. Then he combines his wings, Gale Thruster, and Incarnation power to pull off what has to be the most epic Finishing Move in the entire series!
When he was performing his Finishing Move, the fuel indicator going all crazy only served to add to the effect. And yes (for those unaware), the "blow-like sound with a circular burst of air" was him accelerating beyond the sound barrier.
Black Lotus' theme, Alert Sign, first heard in episode 5. During her fight with Yellow Radio in episode 11, it gains a kickass beat that firmly cements her reputation as one of the best Burst Linkers currently in existence.