Requirements: Reach level 15+ and finish the first half of the Frieza 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 Captain Ginyu if you see him.
Log out and back in to speed up the process.
Speak to him for a test where you'll win Fighting Pose F.
Continue with the game or Parallel Quests and speak to them after each for more tests.
Second: Fighting Pose A.
Third: Milky Cannon
Final: Body Change and your trophy.
Note: Personally I found Ginyu to be the toughest of all mentors as you have to fight the entire Ginyu force in some tests, and this can be very difficult. Kill the members as fast as possible or they'll attack continually and leave you paralysed and taking lots of damage.
You are now free to change mentors.