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