To get this you need to win 500 games through the Multiplayer button on the main menu. They don't actually have to be against humans, you can play private games vs. the ai and it will count.
The fastest way to get this I've found is to go to the map editor and create a custom scenario. For Player 1 place 2-3 castles and for Player 2 place a single spearman in the middle of Player 1's castles. Save the scenario as whatever you want then start up a multiplayer game, set game type to Scenario, and select the one you just saved. Make sure there are two players (one is ai) and start it up. Your castles should kill the spearman and you win instantly.
You can change your civ and the opponent civ to whatever you want to go for the "Win as/defeat civ X times" achievements. These will 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.
The Incredible Team Leader! achievement in Age of Empires II (2013) worth 57 pointsYou have been selected for the Most Valuable Player award 100 times. You have demonstrated great skill in battle, and surpassed that by outperforming the other generals in your allegiance. You are definitely a rising star in this elite group. Congratulations!