You have to defeat Kid Gohan, Picollo, Vegeta, Krillin, and Goku.
To activate the bonus objective, you have to defeat Goku last.
When you do this, there is a low chance that Goku will turn Super Saiyan.
Defeat Super Saiyan Goku for another low chance at getting the Super Saiyan skill.
This is the earliest you can get Super Saiyan, but it is the hardest. Not only do you have to hope that he turns Super Saiyan, you have to hope that you beat him before Frieza dies. Then, you have to hope that he actually gives you the skill.