At the start of each screen you'll find various buildings. Blow fire over them, and then hit them. This'll make them fall down a lot faster. When you burn or knock down a house you get an egg. To beat the other monsters in a fight for an egg, don't jump around and breathe fire, just hold your ground and punch forward. After three or four falls, your foe will stay down. Keep eating, even if it doesn't show any increase on screen, your health will skyrocket.