by travelling through the game with Quina in your party, a new type of magic becomes available: Blue Magic! Blue Magic is a specific type of magic that depends entirely around what attacks your opponents have. That is to say, you quite literally eat your opponents to learn their abilities. There are a number of pre-set Blue Magic spells that can be learned.
Once you've got your opponent's HP down to 1/8th of their total HP (or less), use Quina's "Eat" command. If Quina is in Trance, "Eat" becomes "Cook", which allows you to devour enemies at only 1/4th their total HP. If the enemy has an attack that you do not have yet, it will be learned. If not, it'll die anyway.
Note: There is also a text version of this list.