Easiest done in very first level in hotel. Try to stay ahead of the group and listen very carefully for the sound of a Spitter. This is a good area simply b/c once you hear it, you can round every corner and just fire repeatedly or rain down melee hits. If the horde rushes you, just stay back until they are done so you do not accidently trigger/kill a Spitter.
Edit: There are reports that you can also get this achievement in Versus mode w/ a friend. Simply boot it up, kill all of your AI teamates, and have your friend continue to spawn then be killed until it comes up that he will be the Spitter. Then have your friend let you kill him without him attacking.