Here is my 100% Achievement Guide for The Sinking City!
This is another Missable achievement.
When we are tasked to go the "St Marys Hospital" for the first time, talk to Dr.Grant behind the desk and he will ask you a few questions.
One of those will be "Do you have a headache"?
VERY IMPORTANT to choose "Yes, i think i do"
He will then give you some pills, you lose half your sanity bar but you gain the achievement.
Note, if you say "No, Im fine" You CANNOT ask him again and you miss out unless you reload a previous save but even then, it may not appear. So best to be safe, and say yes you have a headache.
If you want to see where and how this is done in video form, go to 1:04:55 in my Part 1 video.
Hope This Helps!
Part 1
Part 2
Part 3