Here is the full list of all 30 Space Crew achievements.
Complete the campaign
Fully Level up a crew member in two skills
Wipe out the Phasmid Homeworld
Fully level up a crew member
Recover adandoned cargo, found adrift in space
Complete Phase 2 of the Campaign
Have a member of your crew survive 30 missions
Be torn apart by a Black Hole
Defeat 4 enemy champions in a single playthrough of the game
Extinguish 50 Fires by decompressing the ship
Complete Phase 1 of the Campaign
Repair the reactor after it has gone subcritical
Destroy a Mothership
Repair on board systems 100 times
Purge a crew member through the airlock
Defeat 1 enemy champion in a single playthrough of the game
Destroy 250 enemy phasmid ships
Save one or more crew members from certain death by issuing the abandon ship command
Kill 50 Enemy Phasmid Boarders
Lose the ship due to a reactor going critical
Slip away from enemy fighters by performing a hyperjump to a different area
Destroy 100 enemy phasmid ships
Recover a Crew Member that was purged through the airlock before he dies.
Kill 10 Enemy Phasmid Boarders.
Extinguish 50 Fires
Extinguish 25 fires
Destroy 50 enemy phasmid ships
Destroy 25 enemy phasmid ships
Defeat all 8 enemy champions in a single playthrough of the game
Complete a mission and return to Athena with 2 or fewer crew members surviving