To begin with, save the game over the planet, use the Planet Buster weapon tool on current planet. Once destroyed, exit to Main Menu without saving the game file, start playing the game file, and repeat 20 times.
"Quietus" is from the Latin phrase At rest, and is often interpreted as "death". This roughly translates to "Death Star", a probable reference to the (copyrighted) Star Wars-Inspired Superweapon, which annihilated planets before they could retaliate.
The icon for Quietus Star is an alien like form of the Grim Reaper. With three eyes and a star on its chest. The Grim Reaper can be known as "Death" in some occasions, making the star on his chest another reference to the "Death Star" from the Star Wars franchise.