To get this you simply need to play 250 single or multiplayer games with the game type set to Turbo Random Map. You don't actually need to
win the games so you can just start a game against the ai and immediately resign each time. Note that these games to not count toward the Random Map victories achievements or vice-versa.
I would recommend doing this in multiplayer private games to also count towards:
The Day of a Thousand Stories achievement in Age of Empires II (2013) worth 64 pointsToday is a day of great celebration! You have fought your one thousandth battle against online opponents. Order a feast! Make a toast to those who have defeated you as honorable teachers, make a toast to those foes you have defeated, and most of all a toast to your friends and allies who have supported you in your many campaigns.