You will need to play the first act with each individual character: Sam B, Logan, Purna, and Xian. To complete this as fast as possible, focus on the main missions, avoid doing sidequests and explore only to heal, repair, or buy supplies and weaponry. This will take approximately 2 hours for each character.
Selecting Start > Extras > Achievements and highlighting Right 4 Life will tell you which characters still need to be played as.
As a fun fact, this achievement is a reference to the Left 4 Dead game.
Also:
People have reported that playing co-op might bug the achievement and not count some of your characters, in which case just replay chapter 4 with whichever character it says you need to complete. I received this achievement without playing cooperatively and it worked just fine.