This page contains a breakdown of the Legacy Restored trophy in Assassin's Creed: Odyssey. The achievement is granted for upgrading Leonidas' Spear to Tier 6. Below, you can find info about when the game allows upgrading the spear and what are the requirements.
You have to progress to the third chapter of the main thread of the game, during which you visit the Andros Island - that's a big part of the Memories Awoken quest. The Andros Island houses the Ancient Forge of Hephaistos.
When you visit the forge the first time, Leonidas' Spear will be automatically upgraded to Tier 2. The game will also unlock the Upgrade the Spear quest.
In order to unlock the subsequent upgrades of the Spear, you have to obtain more Mysterious Fragments. These are unique artifacts left behind by defeated Kosmos worshippers. Each killed Cultist leaves behind one fragment.
Take your few Mysterious Fragments back to the Ancient Forge of Hephaistos. Place the Spear into the monolith to level it up. Every level requires more Mysterious Fragments.
More info about the Cult is available in Kosmos Cultists chapter of this guide. Another chapter contains info about reaching individual members of the Cult. Collect secret fragments until you're able to upgrade the Spear.