With some careful planning, you can get past the enemies before the boss so you beat them without leveling up or picking up upgrades... I just did! But I collected 30 XP, and used dodge, heals, and bullets. Pretty sure you can do the whole thing on 10 XP if you get lucky, it's definitely possible to beat no-hit (+no heals), no bullets, and no dodge. Now I just have to try again...