Age of Empires II: Definitive Edition (PC) - Achievement - Lone Warrior

Win the Historical Battle "Kurikara (1183)" without forming an alliance with the Hojo clan

This achievement is quite straightforward. Early on in the mission, you will be notified that the Hojo clan are willing to ally with you and you are prompted to send a unit to them to see where this leads - Simply don't do it and complete the mission as you would normally. You start with a fortified city with all the buildings you need and abundant resources, so it's not a difficult one.