Here is the full list of all 38 House of the Dying Sun achievements.
Survive for at least 10 battles in Challenge Mode.
Survive for at least 5 battles in Challenge Mode.
Because this isn't real.
Because I love to kill.
So I could rest.
Because I am not human.
To free the galaxy.
Assassinate The Traitor King.
Purchase all upgrades.
Assassinate Kingsclone B1.
Assassinate Kingsclone A1.
Assassinate Princess Admiral Du Moch.
Assassinate Prince Aum.
Run over a traitor lord's escape pod.
Assassinate Traitor Admiral Alfmundur.
Assassinate Traitor Admiral Anrune.
Assassinate Commodore Ausgauth.
Assassinate Traitor Admiral Bergautur.
Assassinate Lord Commodore Ganuun.
Assassinate Lord Commodore Naybard.
Assassinate Commodore Freyv.
Assassinate Lord Commodore Seigfast.
Assassinate Commodore Elduette.
To avenge the Emperor.
Earn a second wingman.
Earn a frigate for your fleet.
Add a destroyer to your fleet.
Complete at least 1 battle in Challenge Mode
Destroy a vessel while inside its shields.
Complete a mission on Harbinger.
Destroy an escape pod.
Purchase an upgrade.
Earn a new weapon.
Earn a wingman.
Complete a bonus objective.
Complete a mission on Invader or higher.
Complete a mission on Warlord or higher.
Complete host uplink training.