This is story related and cannot be missed. The achievement is unlocked when you complete the first of four possible endings. The four endings can be played in any sequence and the achievement pops when you conclude the first ending you select.
To have the option of playing all four endings without retracing the entire story, make sure you make hard saves at the beginning of the Red Tape mission and the beginning of the Ambrose Intersection mission. Note that you can get all ten of the DLC's achievements by doing only three of the four endings. Consult the spoiler section to see how this can be done.
The four endings are: