In order to get the achievement, you have to clear one chapter (stage) with each of the original four Zombie Army Trilogy characters AND their female counterparts. Not a full five-chapter campaign, just a single chapter from start to finish. You don't have to use Left 4 Dead characters.
The easiest way to do this is to just play a level of a campaign as one character, then when you finish, don't continue - instead go back to the menu, change your selected character, and hit continue to go to the next chapter. You can also do this by replaying chapters, I completed this while backtracking both NZA 1+2 to get the bottles of blood and gold bars.