The solution for each boss and what they can do, and what you need to look out for when you fight with them, can be found in the FAQ section of the walkthrough. If you don't want to get spoilered from the walkthrough, my suggestion would be to make good use of the different elements, and don't hold back with items.
The ice raid should be easier than the nature raid, but how easy or hard the fights are depends on the buffs that you get along the way.
Viewing post in Any tips for defeating all the bosses in challange floor?
I finished the the ice dungeon this morning. But the nature dungoen is truly something. I only manage to defeat one of the supervisors. Does it includes the right equipment for each of the supervisors or just find the strongest equipment? Also, is there any counter for their spells? I've play this game since last year but still can't beat the supervisors till now XD. Help me plz!!!