I've had enough of you! Die!
A person pulls their fist back and yells "FALCON PUNCH!" in a dramatic tone, both to sound badass and to explain just how deadly their blow is to another person.
It was originally used by Captain Falcon in the Super Smash Brothers series of games and it soon became a meme as his move was frequently spammed and just sounded cool. There is also a "Falcon Kick" which is said much more quickly.
Stylesrj's arch-nemesis, Commander Laes has also got the same training, leading to an epic final battle of "Falcon Punch" and "Falcon Dodge"
CivGeneral performed a similar move, which he dubbed "Panzaerfaust", against Wesker. The main difference between Stylesrj's and CivGeneral's move is that CivGeneral applied the Art of the Raging Mountain God, that Ayane taught him. It is basically punching an enemy target instead of the ground.
Because Stylesrj has used the gag a lot in a short space of time, he believes that it's dangerously going to be overused (by some people) and recommends everyone shouldn't do it for at least a while