The Supreme Duck (Aka White Duck) is first shown in Duck Life 3: Evolution and is unlocked after you find a portal leading to the champion when you master all the professional league races. It is also unlock-able in the Arcade if you beat the game with every duck.
Upon finishing the Professional league, a mysterious portal will appear. Upon entering it, your duck will then evolve into the Supreme Duck. You will then have a race against the Champion Duck. When you beat him, you get a throne which the duck sits on, just-for-fun trainings, Domo Kun shootout, and 500000 coins. Lucky!