From Nookipedia, the Animal Crossing wiki
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Medals are the currency used on Tortimer Island in Animal Crossing: New Leaf. They are earned by successfully completing tours and can be spent at the Souvenir Shop in the lobby on the island. More medals are received based on how far the player surpasses a tour's objective, or how much time is remaining when the objective is completed.

The Bronze Medalist, Silver Medalist, and Gold Medalist badges are received from Phineas when the player earns a total of 150, 1,500, and 5,000 medals, respectively.