His "fight" with the kenjutsu club. He doesn't even throw a punch and still takes down the entire club.
First on-screen use of Decomposition, where he vaporizes a wall that was reinforced against magic.
He invents a CAD that enables Flying using Modern Magic. Flying through the use of magic is not new—Ancient Magic practitioners have done it—but it hadn't been done with Modern Magic.
Every. Single. Thing. He does. At the Nine Schools Competition. To put this in perspective, his seniors in the army consider that with Tatsuya as the engineer, he's the resident Game-Breaker for First High. While holding back his true skills as Silver.
He repeatedly comes up with strategies that help his players win by an absurd margin.
He customizes their CAD's to bring out the maximum potential of each player.
He creates an entirely new magic just for a single match.
The unveiling of Restoration
After the competition, he basically single-handily destroys the terrorist cell who was screwing with First High
Kirihara dashes out from the cover of a magic shield and beats down gun-wielding mooks with a combination of hand-to-hand combat and kenjutsu. Then he cuts down a door to silvers in order to cut off the leader's escape. Even Tatsuya recognized his heroic action as surpassing his own (though that may have been to make him look better in front of Mibu).