Here is the full list of all 30 Space Run achievements.
Get 5 reputation points at the end of a delivery
Make your first delivery
Make all deliveries
Get 150 reputation points
Meet Brandon Richards
Make a delivery for each freight company
Buy the three upgrades of a module
Buy all engineering's modules and upgrades
Buy a power generator
Buy all offensive modules
Loot 50 000 hexnuts
Reach 1000 thrust power during a delivery
Recycle 5 constructions during a delivery
Build 5 construction in 5 seconds
Destroy 10 enemy ships
Destroy a boarding ship
Get 10 weapons built on your ship
Use the tactical break ability 2 times during a delivery
Turn 5 pirates into allies in one activation of the IFF jammer ability
Repair 1000 hit points in one activation of the mass repair ability
Destroy 5 enemies or constructions in one activation of the burn ability
Destroy a boading ship with the death ray ability
Destroy 10 enemies or constructions in one activation of the fire rain ability
Bring back 150% cargos or more in a BC delivery
Destroy 2 enemy ships with a single nuke
Use hyperspace ability during the delivery 'Asteroids on steroids'
Destroy 200 pirates during the delivery 'Bloody swarm'
Destroy 25 ennemy ships during the delivery 'Astral journey'
Bring back 10 alien toys in the delivery 'Chaotic run'
Destroy 'The Eye' of Captain Black in less than 60 seconds