Age of Empires II: Definitive Edition (PC) - Achievement - Self-Made Man

Win without allying with Argyrus or Guaimar in the mission "Guiscard Arrives".

You have the option to ally with Argyrus the Byzantine (Purple) or Guaimar of Lombard (Yellow) by sending your hero to either of their castles. To obtain this achievement, you must refrain from either and destroy one of their castles.
I opted for attacking Guaimar as this seemed easier based on the location of his towns and Castle. You can take a couple of settlements with your starting army. Once capturing the settlement closest to his Castle, I built 5 Battering Rams to breach the gates and take down the Castle, whilst using my main force to protect them and kill the units in the town.
Once you destroy the yellow Castle, the hard part is over and you can build your forces up and take the remaining Norman Barons (Red) that you need to achieve victory without ever engaging Argyrus.
As you get reinforcements and resources with each settlement you take, you shouldn't need many villagers to maintain your resources, so build a few to begin with if needed, but remember to kill them later so you can use the population to support a larger army.
You will also periodically receive reinforcements via Transport Ship from the sea.