Not all high tier equipment is obtainable yet. There are different loot tables for defeating enemies, chests, and arena battles, but currently all enemies drop the same stuff no matter in what battle you defeat them. The bonus battle only gives you an additional reward at the end of the battle.
After finishing the fire raid often enough, you'll get the option to raid solo. After winning a solo raid, you can find a new chest in the area (not at the top where the other treasure chests always appear) in which you get the recipe to use the anvils.