Unlike Luigi, Yoshi and Toadette, all who you must unlock in the Special section of the Shop screen, you can unlock Princess peach be finishing the game and rescuing her from Bowser.
Princess Peach features a Floaty Jump, which you can perform like a long jump by tapping and holding down on your screen. Her special jump may be the key to picking up some of those hard to reach Pink coins, and hidden Black coins that you missed along the way.
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