This will be your very first achievement, and the description is exactly what happens/need to do. After you die your first objective will be to follow the "strange ghost girl", you will have a little chat, then need to head back to the crime scene to proceed with your first investigation. You will also get the mindreader and investigator achievements here. Complete the investigation, then you will need to head into the apartment building. Once inside the achievement will pop. Going by the description you would think it would pop as soon as you meet the ghost girl, not the case but seems to be the norm for the story related achievements.