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