Here is the full list of all 43 Adeptus Titanicus: Dominus achievements.
Princeps Maxim has enjoyed the first taste of victory
Princeps Maxim wiped out the Chaos Marines
Princeps Maxim killed the attacking Warhounds
Princeps Maxim held back the Chaos counter-attack
Princeps Maxim supported the Blades of Vigilance Marines
Princeps Maxim killed the Chaos Warlord
Princeps Maxim protected the Basilisks
Princeps Maxim held the defence without reinforcements
Princeps Maxim aided in the hot-extraction of Inquisitor Helena
Princeps Maxim forced the Chaos Warlord Sarame to flee
Princeps Maxim successfully assaulted the Siege Wall
Princeps Maxim held the Siege Wall against the Chaos counter-attack
Princeps Maxim secured the Ordinatus
Princeps Maxim repelled the Chaos attempt to regain the Ordinatus
Princeps Maxim held the space port against the Chaos counter-attack
Princeps Maxim forced Kauleyak to retreat
Princeps Maxim destroyed Kauleyak
Completed the tutorial mission
Killed a Warhound
Killed a Reaver
Killed a Warlord
Captured the enemy's FOB objective
Killed the enemy's Break Their Spirit (BTS) Titan
Won a game on Turn 3
Won a game on a turn after Turn 10
Used the March order 10 times
Used the Double order 10 times
Used the Advance order 10 times
Used the Overwatch order 10 times
Won 5 Skirmish games
Won 25 Skirmish games
Won 10 Skirmish games
Killed enemy BTS in 5 games
Captured the enemy's FOB objective 10 times
Won MP battle with your opponent on 0 Victory Points
Won MP battle by at least 4 Victory Points
Won a multiplayer game
Won a game by Annihilation
Completed 10 multiplayer games
Won 10 multiplayer battles
Completed 50 multiplayer battles as a Loyalist legio
Completed 50 multiplayer battles as a Chaos legio
Princeps Maxim secured the space port