This achievement can be only earned during the course of the levels Archives and Depository as these are the only levels that feature librarians. Killing either a normal librarian or a black librarian counts toward the achievement.
A good tactic would be to stare the librarian down until it walks away, and shooting it in the back of the head. On higher difficulties, two throwing knives to the head will suffice, but this requires excellent aim. The Volt Driver is an extremely effective weapon as well, especially if overcharged.
If you don't have the Volt Driver, you can also take pot-shots at the last (sleeping) Librarian you encounter in Depository before climbing the stairs that takes you to the room with D6's map. The librarian won't follow you into the room with that staircase, so you can use that to your advantage to shoot, hide, and eventually kill it. You don't need to worry about conserving ammunition here because it is the last enemy in the level and the next level will allow you to restock. If you still want to conserve it, however, you could always load the last checkpoint and sneak around the librarian to get your ammo back.