From the Super Mario Wiki
The Third-Degree Card is a collectible item in Paper Mario, where Mario may obtain it by training at the Toad Town Dojo in Toad Town. After defeating Lee and winning the Second-Degree Card, Mario can fight The Master. After defeating The Master, Mario will get the Third-Degree Card. This item proves his bravery and allows Mario to fight The Master again, but in a stronger form. The card has no particular use in-game and is simply a collectible item.
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