The Varmareno Coliseum can be found in Port Brilehaven after finishing the main quest in Martira. This is where you can engage in difficult fights that earn you powerful rewards and also improve your courage.
This guide will only be covering the ranked battle mode, mostly because you can't exactly form much of a strategy for the gauntlet battle fights. The fights in gauntlet battle are a lot more random, with different amounts of each enemy type popping up across all 30 rounds. I'd just wait until you get to the very end of the game and simply breeze through the gauntlet battles once you're overpowered instead.
