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