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