MIPS is the yellow rabbit that spawns in the basement of the castle. He appears first when you have 15 stars and again when you have 50 stars. Catching him will spawn a star each time.
This is how you will be catching MIPS in 70 star and for the first time in 120 star
This is how you will be catching MIPS for the second time in 120 star
In 16 Star, MIPS is used in a glitch called MIPS Clip to clip through the 30 star door to bypass the 30 star requirement. This allows the player to complete the game with only 16 stars if it's paired up with the Backwards Long Jump.
Difference between versions
In the US version, MIPS is slower on his 15 star instance.