The Second Degree Card is an item obtained in Paper Mario after Mario defeats Lee at the Toad Town Dojo. He can only be fought after Mario has obtained the First-Degree Card from defeating Chan. When Mario defeats Lee, he obtains the Second-Degree Card and will be allowed to challenge The Master for the Third-Degree Card.
During events of the game, Mario can speak to an un-named yellow Dryite who has the Second-Degree Card. It has been assumed that he obtained the card when he visited Toad Town and was able to defeat Lee for it.