Here is the full list of all 31 Iron Sky: Invasion trophies - there are 15 bronze, 10 silver, 5 gold and 1 platinum.
Collect all trophies.
Destroy the Götterdämmerung.
Detonate the Überasteroid.
Destroy 10 Hunding ships.
Complete all Indian side missions.
Purchase all upgrades for the Korean light fighter.
Complete all Russian side missions.
Acquire the Banzai heavy fighter.
Complete all US President missions.
Destroy the Wolfram capital warship.
Destroy the Walther capital warship.
Destroy the Tannhäuser capital warship.
Collect 500 salvage.
Purchase all upgrades for the Dundee bomber.
Repel the meteorblitzkrieg.
Destroy 50 Alberich ships.
Acquire the Canadarm heavy bomber.
Destroy 300 Walkyr ships.
Destroy 20 Hanebu IV ships.
Destroy 20 Wotan ships.
Safely escort Renate to the moon.
Destroy 100 Rheingold ships.
Acquire the Spitfire frigate.
Destroy the Herrmann capital warship.
Destroy the Heinrich capital warship.
Destroy 10 Brünnhilde ships.
Collect 100 salvage.
Destroy the Biterolf capital warship.
Acquire the Xerg light fighter.
Complete the tutorial part of the game.
Destroy all drones in the Shooting Range in less than 30 seconds.