Okay, happened to stumble upon some tips in an FAQ, so I think I've got the idea now. Even managed to obtain Simeon's Spell Book from Haruna while recruiting Kate just now.

For others' reference, here are some things to aim for, in order to obtain an S Rank in battle:
- Try to use as few turns as possible. (Doesn't seem to affect it too much, from what I can tell.)
- Try to avoid taking damage as much as you can. The less, the better.
- Deal as much damage
per hit as you can. The total isn't what matters, but the
average damage you deal does. High-power spells and abilities should help immensely, as well as other buffs.
- Take full advantage of elemental tiles. Each time a character ends a turn on their +Affinity tile, you receive one "point" toward getting a higher rank. (Recommended: If a character has nothing better to do during a turn, toss a Bead or cast a Force spell.)
- This one seems to make a huge difference: Try to obtain as many EXP as you can. Having some lower-level characters in the fight swinging at a high-level enemy now and then should help a bit. (Recommended: Try to get higher-level character to
weaken enemies, and then let the lower-level ones finish them off.)
Pretty sure that's it. There are some guides to getting S ranks, though if you plan to get them every chance you get, then I'd personally say you're insane. Haha. There are several levels that you only have one chance to fight in, so it's not like you can just go back later. :S