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