While Wiley College's debate team is famous for its victory in the 1935 National Championship, it's difficult to provide a comprehensive list of *every* college they beat throughout their history, especially from that era. Detailed records from that time period aren't always readily available online.
We know they famously defeated the University of Southern California in the final round of the 1935 national championship. Beyond that, pinpointing all their previous opponents requires extensive archival research into historical debate tournament results.