Note: the 360 solution for this achievement is incorrect, hence why I may be getting negatives.
The achievement description isn't 100% accurate. You are actually looking for "Emmet (Old West)" in case you couldn't find "Emmet Cowboy" in your character list.
In either case, Emmet (Old West) is unlocked in level three, "Flatbush Gulch". After building the wagon and changing into your disguise you will be able to play as Emmet (Old West) so I suggest using him when shooting the bad guys rather than Wyldstyle as his kills during story mode count towards the achievement.
You will most likely not get 30 kills during the story mission, so when you have enough studs, just purchase him in the character select screen in the hub after completing level three, and use him during your free play missions (or play Flatbush Gulch again if you are so inclined). Either way, all enemies count. I don't believe you can get this defeating normal people in the hub.
Let me know if you have questions. Thanks!