Make sure that you have completed the sixth story mission for Bonnie MacFarlane called "Wild Horse, Tamed Passions". This mission unlocks the Lasso.
You can then find a Wanted poster, which shows as a skull on your map. When you accept the Bounty, you will then get a red skull on your map directing you to your target. Kill the other gang members, but make sure to lasso the bounty target. Place him on your horse, and return to town and you will unlock the achievement!