Go to the Menu and click "Battles" to be instantly and spontaneously transported to the Anywhere Battle Arena! (applause) (more applause)
At any point in the game, you can access the battle arena, and challenge either Easy, Normal, Hard, or Hell.
You can choose to fight one battle at a time, or fight consecutive battles. At the end of each battle you get the monster item drops (aka valuable weapon and armor fortifying resources!), and at the end of the arena "course," you get additional rewards (depending on which difficulty you selected.)
One battle at a time lets you fight, well... one battle at a time. (Lols.)
At the end of each battle, it asks if you want to continue. If you do, you keep going until you finish the arena. If you don't, you end off there and you only get the monster item drops for the battles you've already won.
If you do the consecutive battles (or one at a time, all the way to the end) you get additional resources. (I think you get all the rewards that are 100% drop rate, plus "maybe" one of the rewards that's a lower % - one time I got the 100% items and a 30% item, and one time I only got the 100% items.)
So in one run through of the Easy arena, I netted:
Aquamarine
Pretty Feather x3
Beautiful Feather x3
Turqouise
Bat Wing x2
Cold Water (XS)
Dirty Leather x2
Barbecue Set (S)
Sticky Liquid x3
Large Leaf x2
Fluorite
Thick Leaf
Old Cloth x2
Plus the following fabulous prizes: