This is step-by-step guide on how to get Spear of Achilles in Asia Minor proper.
Spear of Achilles Guide
After conquering Lesbos you will land in Asia Minor proper.
If you head northeast you will find a fishing village called Troas (this is also where you’re heading for the main quest while trying to find a traitor).
In the opposite side of the village from where you entered there is a Greek villa with a garden next to it. Inside a tree in the garden you will find your first clue (unless you have ALT toggled to see the outlines of items, this is probably the hardest part of this guide).
Once you have the item in question, head out of the village and to the small peninsula to the east.
Your next destination is back on Lesbos, on the beach on the southern part of the island.
Your final destination is to the north on the westernmost tip of another peninsula. Go inside to collect your reward.