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