DO NOT KILL HER! If you kill her you cannot get the trophy. When you talk to her in the morgue check for a dying patient in the back of the room. He gives you a side quest and the combination to a safe.

Can you save the crown killer?

Cure The Crown Killer (as Emily)

If you play as Emily, you need to make a cure using the notes that you find inside the safe. Go to the lab next door and grab a syringe. Find a dead body near the bloodfly nest in the same area, use the syringe to take a sample of blood and bring it back to the lab.

How do you save Dr Hypatia in Dishonored 2?

Wait for Dr. Hypatia to turn her back towards you, use Blink to get behind her and inject her with the syringe containing the serum. This will heal Dr. Hypatia, you will complete the task and won't lose the chance to receive Ghost status at the end of the mission.