To get this achievement you need to start the mission The Start of the Conservation Movement in Tanners Reach (Tall Trees, marked with a question mark). A crazy man will give you a circle on your map that tells you where to find one of these creatures. Shoot it a couple of times and you have yourself an achievement.
If you want to know what to look for the creatures are large and fairly ape-like.
This achievement is a reference to GTA San Andreas released in 2004, 6 years before Red Dead Redemption. There was a rumor that there was a sasquatch somewhere in the desert but of course there was no sasquatch to be found.
Update: The achievement has had trouble unlocking for people but the website shows many recent winners so the achievement is likely fixed. See the comments for any new developments.