Just like episode 1. This requires you to survive 2 days without dying. You do not have to complete any objectives other than making sure to run to the safe room when it hits 9pm. You can do this in a private game if you like but it will come naturally enough by just playing the multiplayer.
It should also be noted that in order to unlock chapter 2 you have to complete a number of missions in chapter 1. I believe it is 4 missions, but if you cursor over the chapter 2 box it will tell you how many to do.