One of the mini-games in Kirby: Mass Attack is a pinball game, and it has different stages, too. You can see what it looks like in the video below:
Another one is called Kirby Master and seems to involve tapping when your gauge is filled up to the right amount:
A third is called KenKen. The video will be able to explain this better than words:
Mass Attack will roll out in Japan next week on August 4th. North America gets the game on September 19th.