To 'Star' a level, you have to unlock all of the prizes by picking up prize bubbles, picking up presents and coming in first place. You will need to do this for every one of the 71 levels in story mode, which will take a very long time.
Alternatively, you can spend a couple of dollars/pounds and buy the 'Timesavers' DLC pack which will 100% all levels for you, meaning all you have to do is come in first place.
There are seven planets therefore there are seven finales. Below is a list of the names of all finales to save any confusion.
1) King's Castle - battle arena
2) Egg Kartin' - grab 'n' run mini-game
3) Cakes on a Train - versus race
4) Best Before Date - checkpoint race
5) On the Wormpath - boss fight
6) The Funkhole (and Beyond?) - checkpoint race
7) The Garage at the End of the Craftverse - boss fight