Quests with action point rewards

[dracon_steel]

Is there a list of these somewhere?

[flynnjsw]

Action Points are received when you get XP, not for quest completions.

[Falco_Easts]

Is there a list of these somewhere?

See the red bar at the bottom of your screen with 5 circles at the right of it? This is your XP bar. Each on of the those circles represents a rank. Each time you gain enough XP to go to the next rank you gain an AP. When you gain all 5 ranks you can go talk to the trainer and move to the next level.

[Arel]

See the red bar at the bottom of your screen with 5 circles at the right of it? This is your XP bar. Each on of the those circles represents a rank. Each time you gain enough XP to go to the next rank you gain an AP. When you gain all 5 ranks you can go talk to the trainer and move to the next level.

It's worth noting that you DON'T get an AP on the ranks at which you earn a new level (which is when the exp bar goes blue). In other words, you get 4 AP between every level-up.