At the start of the Season of Bloom, you will be invited to the royal hunt. Go to the hunting lodge quickly. Talk to the others there, and then travel to the hunting grounds. Here, you need to kill Poisonous Hydra around the central area of the map, the Enraged Greater Owlbear and the Ancient Wyvern towards the north. Take trophies from the Hydra and the owlbear, but leave the ancient wyvern to the NPCs who kill it. (This is the "Fair and square" part) Return to the lodge and end the hunt, earning the achievement.