I recommend you buy a few mushroom soups from the caterpillar's shop and then try to beat the fox, the weapon she drops is really strong and makes the other boss fights almost too easy. Those mushroom soups restore your health completely so you could run away when your health is low and then restore it once she's out of sight. The easiest way that I found to beat her in her second phase before I got the hang of dodging is to hit her once or twice then run away. Running out of sight of her reduces the chances of her shooting the beam significantly and makes the fight way easier.