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Do you have any more details? What you mention is very vague, was it a dance competition game with random graphics and a couple of character dancers like Dance Dance Revolution? Or was it a battle game with strange creatures carrying swords and spears that only moved when you hit the correct beats (something like Patapon)? Or was it a variety-show type of game (you mentioned mini-game)?
Definitely the Japan-only Rhythm Tengoku, the minigame is called The bon-odori.
https://www.youtube.com/watch?v=iSYFBEKCfp8

All I can remember is you tap to cues and there was one mini-game that I have stuck in my head that goes "don don pan pan don don pan pan"