Here is the full list of all 38 House of the Dying Sun achievements.
To free the galaxy.
Purchase all upgrades.
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
Because I am not human.
Earn a second wingman.
Complete a mission on Warlord or higher.
Complete a mission on Harbinger.
To avenge the Emperor.
Earn a frigate for your fleet.
Run over a traitor lord's escape pod.
Destroy a vessel while inside its shields.
Purchase an upgrade.
Add a destroyer to your fleet.
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.
So I could rest.
Because I love to kill.
Because this isn't real.
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.
Assassinate The Traitor King.