To get Goku, Vegeta, or Gohan to grow one level use a card like Korin, Kami, or Shenron, that fully heals a character when their health level reaches below 5. This is similar to the show when Dende has Krillin tell him that Vegeta needs healed because he's been hurt badly and his healing will make him stronger.
Use a weak character like Kuririn or Chao-Zu to fight Freeza in his fourth and final form. But make sure to not use Son Goku, Vegita, Gohan, or Piccolo.
When you have defeated Freeza the usual credits that show Goku flying will be seen until Vegita appears. Vegita will then transform to Super Saiyjin Vegita and so will Goku transform to Super Saiyajin Goku. Thus, the ultimate battle among the super saiyajin begins.
Super Saiyajin Vegita is by far the toughest boss in the entire game, even stronger than the final form of Freeza. Once you defeat Super Saiyjin Vegita, you get a new ending that is different from the normal.