Treasure Art is rewarded to you when you complete Side Quests (simply known as Quests) from the Adventurer's Guild. Shortly after completing the first area (the Ancient Temple Ruins) you can return to the Adventurer's Guild and you will now receive other Quests from Samuel.
Each quest will give you its details as well as a back-story related to the Quest. Samuel will first task you with returning to the Ancient Temple Ruins and retrieving the bones of an adventurer. The reward for this quest is that you will gain an additional AI controller party member. Returning to Samuel gives you the Help The Honey Buzzards Quest. Return again to the Ancient Temple Ruins and there is a door that Rannie can open if you scroll over it. Inside you will find the orcs you need to kill. The door is in the room with the snake enemies.
Once the quest is completed, exit the area and return to the Adventurer's Guild. Samuel will reward you with your first piece of art, and you'll net this trophy.