For the trick used to bypass the 30 star door in 16 Star runs, see the MIPS Clip page.
MIPS is the yellow rabbit that appears in the basement of the castle, and gives a star when he is caught. He first appears after collecting 15 stars, and once more after collecting 50 stars.
In the Japanese version of the game, MIPS moves at the same, faster speed on both encounters, whereas on the US version, he moves slower on the first encounter.