Amaterasu has (assuming at least two limit breaks for 3rd skill and improved 1st skill)...

A-frame +30% defense buff to party/400 HP regen (1200 HP over 3 turns)
Fire attack to all/inflict darkness (improved version of this with full limit breaking just shortens cooldown by 1 turn, whatever)
Single target B-frame -20% attack/defense debuff

Depending on what you already have/don't have, that can be an insanely useful set of skills. You would have the most familiarity with what you have/need, so evaluate away.

Sol and Amaterasu can work together, if you're asking because you already have Sol. Sol's -20% attack debuff is C-frame. If you don't know why that's important, the gist of it is, buffs/debuffs targeting the same stat but are of different frames do stack.
Downside of such a pairing is that light/fire doesn't get a simple instant boost from any SSR eidolon that I'm aware of.