During any fight against a normal computer (not big boss battles), go into Blast Range, fly above your opponent (keep a good vertical distance between you or you will enter Melee Range), stay RIGHT on top of him/her, and just use strong ki (Y) attacks the entire fight. You can hit them, but they cannot hit you. They may circle around you or move away a couple steps, but simply follow them and hammer away with strong ki blasts (weak ki shots won't hit). This also builds up the charge to use Special and Ultimate attacks while draining their Ki to defend/evade/intercept. When they're in the red and you have enough charge, finish them with an Ultimate for fun. You'll also have to re-do the entire process during mid-fight cut-scenes in Hero Mode and Story Mode. Note: This doesn't work on giant boss battles (Great Ape, Baby Ape, Ultimate Shenron).
The following are skills, super attacks, and ultimate attacks unlocked by completing the corresponding tasks through training under the various masters as a Light type Hero. You may only need to complete the indicating sparring sessions or you may need to complete all sessions up to and including the indicated session: