This quest is given by Festus, an animatronic robot inside Sunset Sarsaparilla Headquarters. Festus is located by following the left wall after entering through the front door. In order to finish this quest the player needs to find 50 Sunset Sarsaparilla star bottle caps and return them to Festus.
Once that is completed, Festus will tell the player the legend of how Sunset Sarsaparilla came to be. When he is done, the game will report that the quest has failed, then the player will be given the quest "A Valuable Lesson".
The player must complete "A Valuable Lesson" in order to receive the Achievement/Trophy "The Legend of the Star".
The story Festus tells about the origins of Sunset Sarsaparilla is not consistent with other information given to the player. He tells the Courier that before Sunset Sarsaparilla was invented, the main choices people had for soft drinks were water or Nuka-Cola. Nuka-Cola was founded in the year 2044, but according to the large bottle at the entrance of the Sunset Sarsaparilla Headquarters, Sunset Sarsaparilla was founded in 1918, over 125 years before Nuka-Cola.
A complete list of Sunset Sarsaparilla star bottle cap locations can be found here
The icon for this quest's trophy/achievement is identical to the icon for Sierra Souvenir Aficionado apart from the Vault Boy holding red bottle caps rather than gold coins, and having blue star eyes, instead of love hearts.
According to Joshua Sawyer, the quest was inspired by his experiences collecting Tootsie Roll Pop wrappers as a boy due to a false rumor that sending 100 special wrappers bearing illustrations of a boy dressed as a Native American shooting an arrow at a star would yield a special prize. The story that Festus tells upon completion of the quest is based upon a story that was sent out to children who sent in wrappers and it shares many common elements. A terminal shows that the rumor about a prize was not created by the Sunset Sarsaparilla Corporation, and was only used to continue the increase in profits that was started by the rumors.
Edit