Go to the right-hand or left-hand corner of the level and remain there patiently. Eventually a vine will come down inches away from you, but not quite hitting you. Just burn it and go back to the corner. Needless to say, you should be as close to it as possible. The vines cannot hit you if you are tucked in a corner well enough. Eventually you will begin throwing your stakes of fire into the creature's mouth. And as for this part; do them one at a time if needed. It is better than losing one third of your health just from hitting his teeth once.