Towards the end of the game, when confronted with the choice to either save the prisoners or Dr. Kavanagh, choose neither at the console. Leave the central detention tower instead and look for a tall box on the lowest level on the outer ring. Moving the box will reveal a secret vent leading to the apparatus about to gas everyone. Destroy this infernal machine to earn the achievement.
The normal way to get this achievement would be to have invested in the Move/Throw Heavy Objects arm augmentation, to lift the heavy tall box, and the Jump Enhancement leg augmentation to be able to jump up several pipes in the area that the vent revealed.
It is possible to gain this achievement even when you are playing a Factory Zero run, without augmentations. First, break the tall box hiding the vent by throwing several smaller boxes at it. Then, once you've cleared the vent, use a small cardboard box to jump up onto the large yellow pipe, another (or the same) to jump up from that onto the catwalk, and a fire extinguisher to destroy the pipe. An example can be found here.