As others have said, advanced job quests would be the most logical way of solving this. Something like staying alive against a mob until it casts the spell you need to learn without killing it, maybe it only casts it as a desperation move at low HP (I'm thinking something like White Wind here), maybe you need to hide behind things to survive it (teach meteor mechanics) and so on.

It doesn't HAVE to just be, "Go to Outer La Noscea, pick a fight with a Coeurl, stand still and yawn until it casts Blaster once."