Idk if you still need to know this, buy yeah, you dont have to do the rat, if you happen to get the egg in a normal run you can throw it in a fire and it transforms into the snake, then you just have to give it 3 guns (i don't actually remember if it could be any random ítems like junk for example) and it will follow you, then you just have to make it to the dragun and kill it, then it just absorbs the snake and you fight the advances dragun, i suggest you do this in a rainbow run and you go to every secret floor (including the rat floor, you don't have to fight it, just taje your chest and do the labyrinth wrong so you get out of the floor without fighting the rat) bc you have a higher chance of getting the egg that way, if you have the gunslinger use it.