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