Written by MSG Commander
The Battle Arena is located in the guild headquarters in Apricus Town.
In the Arena, you can fight different monsters to earn Guild Coins and other prizes.
There is no burning reason to fight in the Arena, other than to get the Heavy Ring (which allows you to walk on arrow tiles in places like Iris' Spirit Tree). The other main reason for completing the Arena is if you want to unlock all the Achievements for the game. The Arena also has the strongest armor in the game (Luxury Coat), but you do not HAVE to have this armor; it's just there if you want it.
Of course, there are some other helpful items you can buy in the Exchange, and you may want to earn enough Guild Coins to buy some of these things, but there's absolutely nothing that you have to have in order to finish the game. (Technically you don't even need the Heavy Ring, but if you want to open every treasure chest then it becomes a necessity.)
The Arena is split into four different levels, or "Cups." Each Cup has three different levels: Easy, Normal and Hard. Furthermore, each level has four rounds (each with its own monsters, and own rewards.)
In order to progress through the Arena, you need to defeat all the monsters on a particular level before going on to the next one. (For example, you must clear all four rounds of Bronze Easy before you can go on to Bronze Medium, and so on.)
The Guild Coins that you earn in the Arena can be exchanged for valuable items in the Arena Exchange (the counter to the far right.)
The most valuable item you can buy in the Exchange is the Heavy Ring, which costs 700 Guild Coins. Equipping the Heavy Ring is the only way you can get to the treasures that are behind arrow tiles - and you can only get the Heavy Ring from the Exchange!
Other valuable items in the Exchange include the Encounter Ring, Repel Ring, Metal Arkstone, and 30 Arkstone, although some of these items can be found in treasure chests, or from enemy drops in random encounters (if you're lucky).
You can challenge the Bronze Easy level as soon as you reach Apricus Town, but the one you'll really want is Bronze Hard (it yields a total of 106 Guild Coins), and to win that level easily, you'll probably want to be around level 30 or so.
I personally don't recommend competing in the higher levels (Silver and above) until after you've completed the True End, and have 3 Maid Weapons (at that point you can put the Difficulty on Easy and just fly through every battle.)
You should make sure to go to the Arena, and buy the Heavy Ring, before you go to Selman Grove (although if you can get it sooner than that, all the better, as there are locations where you need a Heavy Ring as early as Nizana Quarry.)