There are enough goats in the one area to earn this achievement in one hit, rather than finding random goats around and keeping them alive until you find more. Once you progress with the story and visit the Prison, there is an area called "Goat Hill" as shown on the screenshot.
You can access Goat Hill a number of ways. I found it easiest to access the area through the "Snarly Caves". The entrance to the snarly caves is North of your initial starting position and behind a locked gate near the NPC (Edit: NPC's name is Anna - Thanks Cellar Attic)
who is sick and lying in bed
(forgot her name sorry).
Once you get to Goat Hill there are a number of landmines scattered around, so be sure your perceptive character see's them and you are able to disarm the mines. Use the Animal Whisperer skill on three goats to unlock this achievement.
These goats though. They are SOMETHING ELSE. Thats for sure. Thats just a small warning