once you have some star exhibit animals (tigers in the first level), you can click the animals and a smiley face will pop up, then the animal will perform a little action, then several smileys will pop up. after that you can click them again and repeat the process until you reach 250 times. there is no cost or limit, so you can simply keep clicking until you get the achievement. smaller exhibit animals do not interact (such as the kiwis in level 1). i suggest grinding this when you have three tigers, as it takes a few seconds before the animals are available for another click. this way you can rotate between all three animals, maximizing your time usage. there is no in-game tracker, so you might want to count to keep track of it yourself.
if you keep clicking another 250 times you will reach 500 and gain this achievement:
also after about every 10 interaction cycles your concession stands should be missing 1 stock, so i restocked it after every 20 interactions (i was only doing two tigers at a time). that way i would have restocked 25 times per stand by the time i reached 500 interactions. there is an achievement for restocking concessions 500 times, which seems like it might take a while so i figured every little bit extra helps: