From the Super Mario Wiki
The Second-Degree Card is an item Mario receives in Paper Mario after defeating Lee in the Toad Town Dojo, who is available to fight once Chan is defeated and the First-Degree Card is obtained. This item proves his strength and allows Mario to fight The Master for the first of three times. Additionally, there is a un-named yellow Dryite who has a Second-Degree Card as well, meaning that the Dryite fought Lee to gain the Second-Degree Card while visiting Toad Town.
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