Lesser fire spirits. Vicious opponents with fiery magic at their disposal.
Type A Edit
The Fire Elememental can be defeated with relative ease by buffing a Blunt-type weapon with Frost Fusion or by raising its water affinity by other means. Combining Whistle Sting Break Art with Frost Fusion and the Soul Kiss leads to an easy takedown. It is best to have plenty of curatives on hand. It is also recommended to buff the player's armor with Fire affinity (using gems) to minimize the Fire Elemental's fireball attack. The Fire Elemental never runs out of MP as it can replenish it with its Restore MP ability.
Type B Edit
The same strategy for the Boss Fire Elemental still holds. At later stages, or on second playthrough, the strategy is not required.
An easy way to kill Fire Elementals is by casting Enlighten then Frost Fusion-boosted Avalanche. If the spell hits most of Elemental's appendages, it is possible for the enemy to die in one cast—and even if it survives, one or two more hits will finish it.
Fire is the rapid oxidation of a material in the exothermic chemical process of combustion, releasing heat, light, and various reaction products.