Replay any Main Op AI Battle (Pupa, Chrysalis, and Cocoon) after you beat the game.
When removing memory boards inside the AI be alert when moving from one column to another a with an "!" above it will appear. If you reacted in time you will stop half way between the columns and remove a memory board. After you remove the board you'll notice the one you selected will not have been removed.
Go into Mission selection and go to the database. The achievement will pop once you start listening to the 3rd audio tape.