Here is the full list of all 24 Star Hammer: The Vanguard Prophecy achievements.
Destroy a Renmant in Campaign
Destroy an enemy with a laser beam
Destroy a Nautilid in Campaign
Destroy an enemy with a missile
Stun an enemy
Recruit the pilot
Recruit the comms officer
Recruit the engineer
Recruit the science officer
Recruit the intelligence officer
Protect Novus on your own terms
Uncover the Remnant conspiracy
Protect the shipbuilding yards
Evacuate civilians from the Boardwalk
Evacuate workers from DM3
Destroy 100 nautilids
Destroy 25 Remnant ships
Kill a stunned enemy with the Destroyer's laser
Deploy 30 countermeasures
Have a reinforcement join you in battle
Don't lose a single escort during the war
Deploy a strike group with maximum Command Points
Win a skirmish battle
Keep your crew friendly