A good tip to make this less of a grind, try to double hit this also while going for the achievements that requires playing/feeding/washing achievements.
what i did was i placed 3 different expo with an elephant to wash, a 2nd expo with girafee to feed and a 3rd expo with a lion to play with all in the same line.
so i was just running between them doing the other achievements and also putting some mileage on the running achievement, by the end of it i was like 50% done with this and then i just rubber band my controller in a loop and got it easy :)