You get the mysterious case from a man named Satoshi in the Luxe apartments, it is the first apartment on the left when walking down the hall towards Irv's apartment for the mission in Luxe apartments. You will need a lockpicking skill of 4 to be able to get into the apartment. Once you have the mysterious case don't open or discard the case. You will meet Satoshi again near the end of the game after killing Victory. Satoshi is standing with some robots near the exit for Yuma Country Speedway. Speak to him and hand over the mysterious crate for the achievement.