Next to Old Kai is a robot that occasionally lets you take tests. Getting Z rank on all the class tests will unlock the Super Class test. The Super Class test only needs to be passed, does not need to be Z rank.
Tips for getting Z rank.
Perform as many accolades as you can. Getting three throws, 20 ki blasts, and 20 hit combos are very easy to do ones to help increase your score. Finishing with above 80% health, landing 5 and 10 ultra attacks are others to try for too.
Video showing Z rank for each test.