You can unlock this as early as DNA Sequence 9.At the beginning of DNA Sequence 4, you will have the ability to upgrade Monteriggioni to bring prosperity and wealth back to the city. The more you renovate, the more people spend in your city, which generates revenue in the villa’s coffers for you to renovate and upgrade even more.
Your goal is to bring your stronghold’s value up to at least 80%. To do this, you need to upgrade each building in the city. You do this by speaking with the architect in the villa’s workshop. It costs 86,000f to entirely upgrade all the buildings in the city. But this won’t get you to 80% alone. You must also adorn the villa by purchasing paintings from the different five cities to display in the villa, upgrading Ezio’s weapons and armor and finding treasures (feathers, Codex pages, Assassin’s Tomb seals, etc.). Even assassinating Templars raises your percentage. Each time you upgrade the value of the city increases, generating more money.
Your sister Claudia keeps a book of all the upgrades and how much money the city is generating. To look at it, go to the villa and speak to her in the workshop. The book shows your current percentage as well as how much money each area is generating. Once you have upgraded enough to reach 80%, the achievement will unlock.