To unlock the Kingmaker trophy in Assassin's Creed Odyssey, you must first purchase the third episode of Legacy of the First Blade (or own the Season Pass) and download Episode 3.
After completing all of the story quests in Episode 3 of Legacy of the First Blade and unlocking the Bittersweet Beginnings trophy below, you will obtain a broken sword.
The broken sword will need the Medallions of the Ancients to be repaired, so make sure you have killed all of the Order of the Ancients members which will unlock the trophies below:
You will begin the "Remnant of the Ancients quest.
Once you have killed all of the Order of the Ancients members, you will need to visit the Blacksmith (located next to Oikos of the Olympians shop) found at Pilgrim's Landing in the Phokis region. The nearest fast travel point is Ianos Hangout.
Once there, talk to the blacksmith and he will tell you that you will need to return with the 19 Medallions of the Ancients. Hand them over and he will work on the sword once the conversation is over. The trophy will unlock once the sword has been repaired.