The Apocalypse Add-on for Stellaris: Console Edition (JP) has 5 trophies - 2 bronze, 2 silver and 1 gold.
Use a World Cracker to destroy another Empire's capital planet.
Defeat a Fallen Empire's Titan fleet with a Titan of your own.
Destroy another Empire's Colossus while it is in the process of firing on a planet.
Use a Global Pacifier to shield a planet belonging to Fanatic Purifiers, Ravenous Swarms, or Determined Exterminators.
Kill the Great Khan in battle.