A lot of attempting to level magic in battle was *so* slow going. By the time I was finished with all other achievements (except for beating the final boss), my white mage character had Cure at level 12. For a quick way to hit level 16, I bought a bunch of cottages, flew to the first cave (where you get the snowcraft), would enter, teleport out, then heal that character to full, and repeat.
Teleporting out consumes ~90% of the caster's HP, and just keep going until you are out of MP, use a cottage, and repeat. All told, it took about 5 cycles doing that to go from 12 to 16, where my caster had 749 MP (so I could get quite a bit of healing in before using a cottage).