When Man first began to use fire not as a sacred object, but as a weapon of war, it angered a great spirit of flame, this appearing among us as a stallion, cloaked in searing fire, its body of a heat impossible to measure. When, every once in a rare while, the Garamsythe Waterway fills with a thick fog, it is said that the Firemane is galloping its ways and channels, its fiery rage boiling the waters into steam.
Most players would initially expect Firemane to be weak to Ice, however, in Final Fantasy XII, Fire-elemental monsters are weak against Water, not Ice. The party will not have any Water-elemental spells at this point, so the best strategy is to cast Protect and use physical attacks.
Amalia will be using Potions on characters who are low on HP. The water to either side of Firemane doesn't damage him, but it does increase the amount of damage your party can do to him. Attacks that connect with Firemane on the water will do a modest amount more damage; he can be lured out by having your party retreat and wait for him to follow. The boss hits hard, physically, as well as occasionally casting Fire.
To lower magick damage, the party can equip the Goddess's Magicite on someone not responsible for Cure magick. Firemane's special attack, Bushfire, can inflict Poison, and it affects the whole party, so it's useful to have a few Antidotes ready. Amalia may not be able to provide Potions fast enough to balance the damage, so it is advisable to give someone else a Cure gambit.