Obtain a Wolpertinger pet.
There is a quest called Catch the Wild Wolpertinger! – given by Goldark Snipehunter for Alliance – which, upon completion, offers a Wolpertinger’s Tankard item that teaches you of summoning the pet. Alternatively, the tankard can be bought from Belbi Quikswitch – the Brewfest Token Redeemer – for 200 Brewfest Prize Tokens. Both questgiver and token redeemer can be found at the Brewfest camp.
WoW Achievement Guide
The Wolpertinger is a real-world reference to a fictitious animal originating from Bavarian folklore. It supposedly is a small mammal with body parts (e.g., antlers, wings, tails, and fangs) from various different animals attached to it.
If you are short of tokens to just buy the pet, you have no choice but to complete the quest. The effort only takes a few minutes. When you accept the quest, you are given the Wolpertinger Net for catching five of the little critters. To be able to find them roaming around the camp, you need to be drunk or totally smashed via alcohol or a simulation using the Synthebrew Goggles – an item you can ask from Goldark.
A simple macro would make the already easy quest even faster to accomplish:
/target Wild Wolpertinger
/use Wolpertinger Net
The Horde equivalents of the Alliance questgiver and token redeemer are Glodrak Huntsniper and Blix Fixwidget, respectively.
The achievement cannot be obtained if you obtained your pet as a battle pet that is sold from the auction house.