Lucifer has surgically implanted you with Magatama, demonic leeches that magically alter your body and soul to become more powerful, growing with experience to make you a being that can kill Gods. This has no upper limit, with the original Demifiend growing in power until he killed a being that created and destroyed millions of universes every second.
The Magatama also give you unique abilities and magic as they grow, such as being immune to all physical damage, or being able to cast mass Almighty "make your save or die" attacks, not to mention increasing your stats.
You need no equipment to perform the feats of the COMP or Demonica, being able to negotiate with, bind, and fuse demons yourself.
You start at level 1, slightly above peak human and barely able to kill nature spirits, but you start with all of the Magatama unlocked, giving you a boost to your starting power that the original Demifiend only received on New Game Plus.