The easiest way to obtain a food item is to just buy one from the store. Go to "item packs" in the shop. Purchase any pack although recruit pack is the cheapest and will always net you 1 food. After you have opened your pack back out to the main single player menu and select "dragon roost". The 4th selection down is "feed dragon". Just click this and give him any food in your inventory and the achievement will unlock.
You can also obtain food as a random drop from killing enemies in levels but this is the fastest and easiest method.