Thanks to AgriusRage for helping me with this one. SPOILERS AHEAD.
After you first go to the FBI you will meet your boss, then head to meet Halperin. You'll ride an elevator down. As the doors open look left to see a small red chair in the corridor. Go over and pick up the glasses that are sat on it - do this BEFORE progressing any further down the corridor or you'll miss them.
Now much later on, after you find Halperin's locket there will be a number of scenes when you return to the FBI. In one of them you'll be sat in the room with the PA, look over at her and she will look at you and gesture. The achievement will pop then. This happens BEFORE you go to meet Halperin on top of the water tower for the last time.
If you DON'T get the achievement at that point (and assuming you picked up the glasses) then it may also unlock right near the end of the game, when you find yourself sat down having a meal with the PA (after you end up in jail and take the drugs). So don't be alarmed if it doesn't pop in the first instance as it may well pop at the second attempt.