-Pause the game and select the options menu. Then change the targeting mode to expert.
Step 2 (I used a bounty specifically the First Bounty at MacFarlane's ranch)
-As you approach the general area of the bounty you should see red dots (enemies) on your mini-map.
-Stay far enough away that you are not detected but close enough that you can line up a headshot with your repeater carbine (any long range gun will suffice). Once you pull the trigger (RT) and the enemy dies, the achievement will unlock.
-You can also use Dead Eye to make this easier.
-Don't forget to change the targeting mode back to your desired setting after the achievement unlocks.
-This must be unlocked in Single Player (Thank you Curtieson for confirming this)