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This achievement can be earned at any time during the course of your playthrough.

You will first obtain the Heart during the Void sequence at the start of Mission 2, Edge of the World. In order to listen to the secrets of an individual, all you need to do is equip the Heart and press [ Register or Signin to view external links. ] when aiming the reticle at an NPC. While the achievement description indicates you must do this on forty different people, progress carries over upon death. This means you can make a manual save, listen to the secrets of five NPCs, get yourself deliberately killed, and then repeat this process on the same five individuals eight more times.

If you desire to get this naturally, there are hundreds on NPCs throughout the game's nine missions that you can eavesdrop on. Regardless of how you do it, the achievement will unlock after the fortieth secret has been told.