When you first head to the world map you will be presented with two missions.
The Hoon Family residence or the Arapaho Caravan.
In order to get this achievement you must go to the Hoon Family residence.
Once you have cleared the enemies head behind the main house to find a two headed goat in a pen (Billy and Jean), tame the goat (Animal Whisperer rank 1) and then keep it alive as a companion until the end of the game.
As an edit to this I have not yet tried leaving the goat at the Hoon residence until near the endgame and picking him up then so not sure if this works or if you must get him at the first encounter.