Requirements: Reach level 40+ and finish the Buu Saga.
After meeting these requirements, when you enter the city check all 3 main areas for mentors (There's only ever a maximum of two) and speak to Gotenks if you see him.
Log out and back in to speed up the process.
Speak to him for a test where you'll win Galactic Donuts.
Continue with the game or Parallel Quests and speak to them after each for more tests.
Second: DIE DIE Missile Barrage.
Third: Super Ghost Kamikaze Attack
Final: Super Ghost Kamikaze Attack and your trophy.
You are now free to change mentors.