I found (warning i'll list them all)
1. going up to floor 0
2. hp 0
3. sanity 0
4. losing to a bat, then sanity 0
5. Lose to the rats king
6. beat the rats king, then wear the rats king's crown (the one you found)
I believe dying and/or fleeing might not be part of the 6 bad ends, and that would leave us with either Ratty or the gruff adventurer as alternative bad ends.
For Ratty, a scroll that turns the rat back in his human form might help, like the potion of purity do for the playable character. I found a "scroll of identity" once, but I couldn't find Ratty to try it out.
For the gruff adventurer, he claims he will make us a warrior or something "one day". So I guess we should weakens the playable character enough for the adventurer to take over, but I did not succeed. I tried to succumb, to resist, to take the shoes off, to leave after being possessed, if he is an ending, I do not know how to reach it.