Here is the full list of all 16 Captain Starshot achievements.
Board your first ship.
Get past the first sector.
Get past the second sector.
Get past the third sector.
Save the Galaxy.
Assign an ability to a crew member.
Acquire a new crew member.
Assign a modification to Captain Starshot.
Hit an asteroid in space.
Encounter the police. They don't like it if you get lucky.
Finish the game without any crew members.
Have none of your crew members die in a single run.
Have six crew members in total.
Fully load out a crew member with abilities.
Have 30+ shield points in total.
Meet an untimely end on a ship.