To unlock the Birthright trophy in Assassin's Creed Odyssey you must first progress the main story line until you
You will then receive a side quest that takes you in search of
Complete the simple mirror puzzle in the ruins by smashing down wooden barriers and pulling obstacles out of the way of mirrors until you can open the ancient door. Head all the way down the path past lava and ancient ruins until you see a figure. The trophy will unlock at the end of the scene.