This can be unlocked both online or offline. You must play as 4 from start to finish.
For offline you will need to have 4 controllers. These can be any controllers, such as instruments
Just start any level having 4 players joined in the game at the puppet select stage, you can do any level including the fast minigames such as Chicken bombs but you MUST play on Family for it to count as a team.
The achievement pops at the end of the level.