You unlock the achievement by going to the mansion in The Ambrose Intersection Mission and using a special terminal to execute the NDA Protocol which destroys the synthesizer. This is one of four possible endings in the game although, if you choose the right three endings, you can get all ten of the DLC's achievements.
The four endings are:
Acquire the journal during the Red Tape mission. In the dialogs with Minnie and Olivia, be noncommittal. Your choices in the conversation don't matter because the outcome will be determined by your action.
When you have control of your character for the Ambrose Intersection mission, proceed to the mission's objective marker on the mansion, ignoring the second mission's objective marker on the facility. You will meet up with Minnie. There's no need to converse with her. Since you are not trying to achieve a compromise, the conversation will eventually lead to combat anyway. Choose the option to attack her directly. After you kill her, go to terminal behind where Minnie was standing when you conversed with her. Use it and select, "Execute NDA Protocol." The achievement will pop.
Alternatively, you could converse with her. If unpersuasive, you will end up having to fight her, after which you could execute the NDA Protocol on MInnie's terminal. If you are persuasive, you will get a third mission objective--Find a compromise between Minnie & Olivia. This does not nullify the NDA option. If you make a save file right after the dialog, you can revert to it and use it for two endings. First, you can go up the stairs and use the terminal. Minnie will protest, but you can use the terminal to execute the NDA protocol unlocking the achievement. Then, you can load up the save file you made after the persuasive dialog, go to Olivia and convince her to reconcile with Minnie. This will unlock the following achievement:
Note that although executing the NDA protocol, unlocks the achievement it does not complete Olivia's ending. To do so, go to Olivia and converse with her. This will finish the story. If it is the first time you have completed the DLC with any ending, you will unlock: