This one glitched on me (progress bar on achievements page suggested 1/3 despite performing every interaction multiple times).
The glitch happens if you do the tutorials first, so the only way to get the achievement is to jump straight into campaign mode and do the interactions before doing anything else.
Edit: Since the Xbox One update allowing us to manage our own storage this solution is mostly redundant, as you can now delete your save data and start up a brand new game.
Head straight into challenge mode, do the 3 interactions (feeding, washing and sensory) and the achievement will unlock
.
For those who are coming to the game from the start and don't need to worry about the glitch but want to know how to do each of the interactions, these are the interactions and the animals you need to adopt to be able to perform them (thanks Bumfluff1202):
-Sensory enrichment - tigers, chimpanzees, or lions.
-Hose interaction - elephants, bears, hippos, or rhinos.
-Feeding interaction - elephants and giraffes.
In any game mode, click in an empty space of the zoo to build an exhibit, choosing one that is appropriate for the animal you intend to adopt. (You can click into a current exhibit to look at the 'adopt animals' menus to see which exhibits they like). Alternatively, if you open one of the challenge zoos, there will likely already be some exhibits and animals available for you to build the sensory toys in.
When the exhibit has been built, through the menus you will have options to build enrichments such as feeding stations, toys and sensory enrichments. Choose the sensory toy appropriate for the animal as detail above and build it in one of the available spaces. If it is a small exhibit that was already built in a challenge zoo, you may need to remove an existing toy or feeding/cleaning station to make space. Come out of the top down view if you haven't already (press Y on a path) and walk up to the exhibit where you will be able to feed, wash or play with your animal. Bear in mind, it sometimes takes a while for your animal to head over to you, so just be patient.