The below video shows the achievement unlocking. Adam leaves A Block and goes to B Block. In B Block, he finds a yellow B Block prisoner jump suit hanging in a locker in a storage room. Putting it on unlocks the achievement.
For reference, Adam has a crude map that he acquired during his conversation with Flossy. The video shows the way through venting that can be accessed from the shower. This route has some risk. Adam emerges between two large fans. The one on the left is moving. The one on the right is not moving but a short circuit has electrified the floor. Adam must move quickly forward, open a small door, and turn off a circuit breaker. This removes the hazard and stops the moving fan allowing him to go beyond it into the storage room where the achievement is obtained.
Adam does not need to go through the vents. He could use the access card on the panel pointed out at the 1'45" mark in the video to go straight into B Block. He would have to be stealthy to avoid detection because he is not authorized to be in B Block. The storage room with the jumpsuit would be to his right if he were to enter B Block using the access card.
Without augments, Adam would need to use a multi-tool on the door of the storage room. Adam is shown acquiring a multi-tool at the 40" mark in the video. The Neuropozyne required for the trade can be found in a hiding place inside Cell A320 to the right of the door.Note:
Players who do not yet have the Quid Pro Quo achievement by trading booze to the inmate at the exit to the yard, could get it by trading Nupoz (Neuropozyne) to the inmate in cell A214. If not previously obtained, this achievement will unlock when the trade is made.