Tamaki repeatedly holding her ground against Ishibashi-sensei. When her first strike - a one-handed one which qualifies as a CMoA in itself - is called shallow, she executes a far more difficult and stylish one-handed evading strike.
The legendary throat strike at the climax of episode 17, complete with battle screams and a silhouetted slow-motion of the brutal blow that lifts the opponent of their feet that one would expect from a shonen action show rather than a light-hearted character-driven sports show.
The fight between Ura and Ume in the manga, which takes up an entire volume and ends with Ume barely winning. They both collapse at the end.
The final battles of Miya Miya and Carrie. This time, in an official tournament match, Miya Miya defeats Carrie. She also stood victorious once more in an unofficial match afterwards against Carrie, who used her dual swords.