This is the same as the similarly named achievement from the original 360 version.
Here is the original solution from gordoncenafa.
Story Based Cannot Be Missed
*** Spoiler - click to reveal ***As you progress through the story far enough you will come to a point where
Keith David realigns with the Saints and gives codes to Matt Miller, and in doing so Matt gives the codes to CID and causes him to go haywire and essentially transports the player to another 1950's simulation
After being transported again to the 1950's style simulation for the second time, you must track down Kinzie, where the first version you come to is revealed to be a decoy. After that you must chase down a police car with another decoy Kinzie in it.
The decoy then tells you to go to the town square, where Cyrus Temple is the mayor, and has organized a rally.
*You must then reprogram the speakers broadcasting Cyrus' speech to drown it out with '50s music.
*After reprogramming the first speaker, Matt will give you a Dubstep Gun so you can fight off propaganda trucks that try to run you over.
*When you finally finish reprogramming all of the speakers, Cyrus Temple goes to the stage, where the real Kinzie is in a poodle skirt.
*The reprogramming causes a glitch that makes the crowd and the real Kinzie dance, and Cyrus loses his temper and then attempts to kill you.
*Matt Miller will give you a reskin of the Dubstep Gun, which converts it into the Pop Skin.
*After defeating Cyrus, You and Kinzie escape.