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