how i beat the game (eventually): avoid the four mini-bosses at all costs. Just go and kill the formations that suit you best. That way, you can build your ship to a high level without too much risk. Don't worry if you screw up. If you do, most 'rooms' next to the one in which you got killed / sustained heavy damage will offer you safe bubbles, which you can use to almost get to your previous progress (kinda like an autosave). When you are fully upgraded, just go from room to room until you find the boss. He is easy :p
For those still wondering how to get the medium badge: the key is to NOT sell the magic items you find. By the time you get the hard badge, you should have multiple items with the suffix "of death". Just equip it and the medium badge will be granted.
Wow Boewz, thank you.