The South West region is definitely the best place to get this as well as the SNIPER achievement. Why not get both at the same time?
This region is relatively flat and not so condensed with trees that block your view. I used the Durango Springs Open Hunt area to start, there is a tall hunting stand ahead of you once you start this area. This stand can help you get up high enough to thoroughly scan you surrounding area. Either way, the Southern portion of the hunting area is more barren of vegetation, so it's easier to spot game and get a good shot.
You should use the .338 Mag rifle with the Polymer Tips bullets and of course, a 2x scope.
Once you start the hunt, find an area that is higher in elevation then most around you, like the hunting stand directly in front of you or the hill (Bedding Area) just to the East. Now, use your binoculars to scan the area to see if you can spot anything off in the distance. If you can mark it, be sure to do so, if the target is too far away you won't get any info on the animal - that's at about 270 with the 5x binoculars.
- If you are having a hard time with the binoculars, then you can run around to get an indicator of a nearby animal. Then mark it and backtrack until you are at 200+ yrds from it.
Either way, be sure you are at least 200 yrds from the animal and have a clear shot at it. Be sure to hold your breath as you are aiming.
- You may have a hard time seeing the target with the 2x scope so try to pick out the color change, (the pronghorns are easier to spot). Try to aim towards the front of the animal while it is showing its side, makes for a bigger target. The scope dot will highlight red when you are close to or aimed right on the target.
Once you hit the target, give it some time. The target may die even if you shot it in the hind leg, you never know. Any organ hit will cause the animal to die given enough time. Mine was a gut shot from about 310 yrds, took a little longer for it to die but it did. I simply stood still until the notification popped up saying "Claim the Trophy"
The achievement unlocked as soon as the animal dropped. I only hit it once. I also unlocked the SNIPER achievement with the same shot. I am unsure if you can hunt a female animal and still get the achievement, I would imagine you can since it is still a big game animal. If anyone can verify whether or not a female counts, please leave a comment.