You have passed the first battlefield key, and the next you will find shortly.
<span class='standouttext'>Spoiler : </span><span class='spoiler'>The first BF key is in a locked chest in the cell block you started in, with the key in the left spider cell in the arena.</span>

In general, you do not want to fight melee only against opponents that use ranged attacks. In this fight it really helps if one character is using a bow/crossbow or magic to attack from a distance. The melee character will still do a bit of chasing, but with the ranged attacks, the mages will not be able to run away as well, and will take damage as they try.