Realms of Arkania: Star Trail

You can purchase a battle axe from most weapon merchants the cities for about 11 ducats. Once you have it, press to open your inventory and equip it onto one of your characters.

Then, you just need to have that character attack someone in battle with the weapon. Venturing outside the city (fast traveling from the map) seems to be the easiest way to engage in combat. Once your character has attacked an enemy, the achievement will unlock.

Even if you use the auto AI to fight the battle, it will still register for the achievement, so no worries there.