WARNING: SPOILERS AHEAD! PROCEED WITH CAUTION
Here are the endings I've discovered so far (numbers are arbitrary and not tied to the in-game numbering)
1) Demoted Ending: During the Azri battle, don’t die but also don’t kill her yourself. When asked, give up the amulet.
2-3) Naafiri Endings: Stay in her world:
On equal terms, OR
As her pet.
4)Genocide Route (Update 0.61): Start a monster genocide =) and ultimately sacrifice yourself to the skeleton furry (the goddess of death).
5) Escape with Azri:
Heal her properly and make sure she has food. Then, escape together and live with her
6-7) did not discover yet, but I believe one of them is the non working kill Azri ending.