As soon as you get your Tenko, the merchant starts selling snacks. Buy some, then go to the Tenko and press Square to feed it. You can do this once between each mission, do it 10 times for the trophy.
Candy and dumplings can change your Tenko's voice and colour. The item descriptions tell you the exact effects of each one. You have to feed it the same thing 2-3 times in a row to make it work.
Rice meals don't change your Tenko, but they do improve its mood. A happy Tenko will bring back more/better items from the battlefield than a sad one.