Simply play the multiplayer for 200 matches.
As every mode under the "Online" section of the game counts towards this. (KotH, Versus, TowerBattle, etc.) it doesnt matter what you play.
You dont even have to win the matches you just need to complete them.
If you want to, you can even play with a friend by choosing :
"Online" - "Versus" - "1v1" - "Private Match"
and it will still count towards the achievement.