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