Zoo Tycoon

Select a challenge to play. Build a medium or large Savannah exhibit and adopt 3 or more elephants. Edit the exhibit to include a "Feeding Interaction". This is what is necessary to complete the achievement, but to keep the elephants healthy in-between feedings, you can also build a Hose Interaction to keep them clean (there's a similar achievement for that as well), and an appropriate enrichment (I chose the Engraved Punch-bag Rope Toy).

Once the exhibit is set up, walk to the Feeding Interaction, look in the direction of the animal you wish to feed, and then pick up a piece of food. When the elephant arrives, Offer it the food. It will ask you to do that two times per interaction to fill up the feeding bar. When the elephant moves away, look in the direction of another elephant and repeat this process.

The Interaction is a bit slow especially when you are waiting for the elephant to walk over to you so it can take a couple of minutes for each Interaction. Put some good tunes on or snap another Xbox app to pass the time if you like

The achievement will pop immediately after your 25th Feeding Interaction.

I chose the elephant because you can also get the similar "Shower Time" achievement by using the Hose Interaction. The elephant is available from the beginning and utilizes both Interactions (not all animals can use them). If their hunger meter is all the way down when you start it can take several feeding interactions to fill them so by the time you get around to all of them, it's time to feed again!

The Medium Savannah Exhibit costs $2,400, the African Bush elephant starts around $1,800 each, and the Feeding Interaction costs $1,000, for a grand total of $8,800.

You can do this achievement with any animal that can use a Feeding Interaction exhibit item.

If you need to know how to add the Feeding Interaction to an exhibit:
Walk next to the exhibit wall and the "Edit Exhibit" button prompt will display.
Follow the cues as such: Exhibit Items --> Interactions --> Feeding Interaction