Unmissable storyline achievement. Occurs after leaving the batcave and destroying Dr. Young's notes.
I was stuck trying to find the note for 8 months. It's embarrassingly obvious now. In the main hall of the Eastmost Building, there's two doors. One is obvious and to your right, the second is hidden behind and right of the large statue. Do the second one first. You need to get Dr. Young's fingerprints, then go to the library.
Copied from Trueachievements.