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