Here is the full list of all 31 Space Tyrant achievements.
Won the Astron war Mission with starting artifacts
Filled every Perk slot during a Campaign
More than 12 Crystal maximum
Averted 10 Disasters
Win 50 Missions
Earned all Bzzerk Union unlocks
Unlocked the TechnoSlug Party
More than 750 credit income
Unlocked the Bzzerk Union
Won a Mission without playing a card
Captured all three Omega Cores
Win 10 Missions
Used the Death Ray 10 times in a Mission
More than 75 research income
Averted a Disaster
Defeat the Astrons
Unlocked the Hoplite Clans!
Earned all Hoplite Empire unlocks
Earned all Hoplite Empire cards
Earned all Hoplite Empire tactics
Earned all Bzzerk Union cards
Earned all Bzzerk Union tactics
Earned all TechnoSlug Empire unlocks
Earned all TechnoSlug cards
Earned all TechnoSlug tactics
Crushed 50 Rebellions
Win 10 Campaigns
Win 50 Campaigns
Executed a fleet commander
Won with less than 10 Tyranny remaining
Win 100 Missions