You can get this achievement in Act 2. You will need the talent Pet Pal on one of your characters (and Spirit Vision, obtained during the main quest, if you want to complete the quest). This solution will contain slight spoilers for the quest Counting your Chickens.
East of Driftwood, there is a chicken coop. Talk to the chicken called Big Marge to get the quest Counting your Chickens. Big Marge will tell you that their eggs have been stolen and you should retrieve them. The eggs are located to the North (marked on your map). When you get there, you will have to fight some Voidwoken. After the battle you can take the last surving egg back to the chicken coup. Now go somewhere else and revisit the chicken coup later.
Once you return to the chicken coop, there will be only one chicken left alive. Talk to the chicken Peeper and the achievement will unlock. Peeper will now follow you.
Note that this quest can be quite buggy after this point.
Have a look at the wiki for more information. Linky