Walkthrough

Talk to Sendak to call your dragons, the Dragonkeeper (who'll explain about types of food) and a salesman. Feed the dragons (I still don't think you should buy anything). If you won weapons or armor in battle, talk to the salesman and equip them on your party, then feed the old stuff to the dragons. If you got any elemental grasses, first feed them to the dragons who already have that elemental; it's better to get one strong attack than a bunch of weak ones. When you're ready, talk to Sendak again.

This battle has two added complications: first of all, the various walls and structures will heal enemies at the start of their phase. Second of all, those big cannons will be a big pain to you. Head for them as soon as you can. Use Thunder Gaze or Inspire on the field to destroy the structures they're standing on and cancel their HP regain. Also, make sure not to use Dance near the bridge, or you may get unlucky and destroy it! ^^; Use ice magic to get across again if that happens. Groyer has no long-range attacks, so soften him up from a distance then go in for the kill.