This mission is a side quest received at the Sunset Sarsaparilla Headquarters when you talk to Festus, the robotic cowboy mascot in the lobby.
You'll need to collect 50 Sunset Sarsaparilla Star Bottle Caps to complete this quest. There are 100 in the game that are in set locations, as well as a 10% chance of getting a star cap randomly when you open a bottle of Sunset Sarsaparilla. Finally there are random encounters with collectors which could yield additional caps, depending on how unethical you are. A collector named Malcolm Holmes may approach you to discuss the caps, who you can pickpocket or kill for his collection. You may also randomly interrupt a fight in the wasteland between Tomas and Jacklyn who have a number of caps between them. Once you have 50 caps, return to Festus for your "reward".
Don't panic when the quest "fails". Talk to Festus again to get your real prize and you'll get another quest called "A Valuable Lesson". Complete this second quest by going to the prize closet and picking up the holotape, and you'll get the trophy. Make sure to pick up the unique weapon Pew Pew while you're here!