There's a cursor that moves to the left and right. If you have a good timing and press the action button when the cursor is at the center, you inflict more damage.
Yuna - Monster Summon
Yuna summons a beast with their overdrive gauge at MAX
Wakka - Slot
Wakka attacks depending of the color of the atribute the slot chooses.
Kimari - Enemy Skill
You can acquire enemy skills with the Dragon Sword ability and (of course) you can use them later vs. your enemies.
Lulu - Temptation
During acertain amount of time you have to make combinations with the R3 stick. Depending on the combination, Lulu makes a combination of spells.
Auron - Secret
You acquire auron's overdrive techniques from the different places you visit. As the name of the overdrive says, you have to find the secret places.