Circle of Regality

The Circle of Regality is the Royal Wraith's elliptical crown, found on sublevel 3 of the Royal Wraith's Palace. Being made of pure gold and amethyst gems, it weighs quite a bit, needing 100 Pikmin to carry it. However, since you'll only have Purple Pikmin with you, it only requires 10 Pikmin.

Strategy
Defeat the Royal Wraith to win his crown.