The Wandering Village

The ability to pet Onbu is acquired through the research tech tree, accessible through . Once in the research menu, scroll over to Onbu researches using and progress through the following tech tree:

Onbu Pharmacy -> Onbu Doctor -> Pet Onbu.

To learn Pet Onbu, you will need 3 knowledge. Extra knowledge can be found a couple ways: by sending scavenging parties out into the map (requires Scavenger Hut,) or as a reward from random events in settlements, ruined settlements, forests or mines.

Once the skill Pet Onbu is researched and you have an Onbu Doctor built, you can activate it from the bottom menu visible if you're in the Onbu view (where you can see the whole creature at once). Upon using the ability the first time, the achievement should pop.

Of course research takes time and you will need to keep your village alive during this process, but assuming you don't completely goof, you should be able to easily reach this along the course of one playthrough. This achievement is not difficulty-dependent and I was able to unlock it on Tutorial difficulty.

In case you need a video guide, here's one (credit to Quick Tips):