If you play the corresponding mini-game and finish in first, second, or third place, you will unlock three, two or one move:
Balance Game: "EXE Beast", "Gamma Blade", "Youshijin"
Hit Down: "Mad Struggle", "Aerial StunEdge", "Love"
May's Dolphin Show: "Do You Want To Suffer?", "Bargain Of Street Meeting", "Phenomenon EX"
Note Capture: "Chemical Love", "Invite Hell", "Mappa Hanti"
Sword Master: "Whatever Is Done, A Fellow No Good Is No Good", "Tyrant Rave Ver. B", "Bellows…"
Venom's Billiards: "Starship", "Sliding Head", "Single Blow Of The Reform"
Yo-yo Polish: "Tandem Top", "Axl Bomber", "Potemkin Buster"