Monsters are not the only thing you can battle against as an Envoy. You can test your mettle against other Envoys of Gaia in the PvP arenas. To join an arena click on the crossed swords icon near the mini-map.
The resulting PvP window will display a schedule of what times the arenas are open as well as the prizes and rules. If an arena is open you can click the Join button to be transported to it.