To unlock the Overcooked trophy in Overcooked!, you must simply leave an item of food cooking for too long so that it sets on fire, and then extinguish it with a fire extinguisher.
You can unlock the trophy on level 1-1. Chop up an onion or tomato and put it in a pot to boil. A green bar will begin to fill up to show the cooking progress. Leave the pot on the flame until it beeps and eventually sets on fire. Once it is on fire, grab a fire extinguisher and put the fire out.
This trophy will most likely unlock naturally as you play the game, so don't feel like you have to rush to get it out of the way.