This achievement is for playing episodes 1-36. All you need to do is complete them. You may complete them in single or multiplayer.
To check your progress check the episodes section of the game. This is in the part of the game where you hit "A" to join. Instead of hitting "A", hit "Y" to look at your episodes. Any episode with a checkmark next to it has been completed. When 1-36 are all checked off you will gain this achievement.
EDIT: it seems that if you play locally with another player you may mess up the system that registers which episodes you've finished. If your achievement does not pop and you have played locally, make sure that you replay the episodes (in solo mode) that you played with another player. (Credit to TheDude722)