Before the quest, make sure you're as strong as you can be, using the witch - get to 4 on all the elements.
Next thing is getting like... 15 fire potions and 8+ on each of the other elements. it's better if you want to go for "certain" and just buy a bunch more (considering you'll maybe have to do the dungeon more than once).
Now you need to know that those potions can get you OVER your max state in an element (up to 8), so before the 1st battle, drink a bunch of a single element (just not fire) to get it high, maybe even max it, then just spam it in battle until you win. after the battle heal up on your low elements using the other potions (especially fire since that is where you'll be hit the most), then proceed to next battle. repeat until you get what you want