After the first map that's covered in ice there will be elk statues situated around the map that give you health, to get the achievement you'll have to not use these until you beat the dragon boss at the end of the third area that's green, foggy and has the druid enemies. I was decently upgraded by the time I did this and it's an important note that I did buy the elk antlers from the shopkeeper to heal me for 50 health and this did not void the achievement.The boss isn't that hard if you stick by his legs and get used to dodging his attacks. You could skip some events/items to avoid enemies to save on health too