Here is the full list of all 53 SOL: Exodus achievements.
You destroyed 20 ADP's.
You destroyed 15 ADP's.
You destroyed 10 ADP's.
You completed a mission using only guns.
You successfully completed the Titan mission.
You performed a heroic action during the Titan mission.
You took out 50 enemy missiles.
You successfully completed the Saturn mission.
You hacked 10 enemy capital ships.
You took out 25 enemy missiles.
You successfully completed the Uranus mission.
You performed a heroic action during the Uranus mission.
You downed 100 COD fighters.
You successfully completed the Neptune atmosphere mission.
You performed a heroic action during the Neptune atmosphere mission.
You destroyed 5 enemy capital ships.
You protected 10 transport vessels.
You performed a heroic action during the Neptune orbital mission.
You successfully completed the Neptune orbital mission.
You served at a Veteran's level during the Neptune orbital mission.
You successfully completed the Triton mission.
You performed a heroic action during the Triton mission.
You destroyed an enemy capital ship.
You successfully completed the Pluto mission.
You served at a Veteran's level during the Pluto mission.
You served at an Elite level during the Pluto mission.
You performed a heroic action during the Pluto mission.
You completed a mission without docking or ejecting from your fighter.
You hacked an enemy capital ship.
You protected a transport vessel.
You downed 20 COD fighters.
You survived the UCS-1 mission.
You served at a Veteran's level during the UCS-1 mission.
You served at an Elite level during the UCS-1 mission.
You performed a heroic action during the UCS-1 mission.
You took out an enemy missile.
You downed 250 COD fighters.
You protected 25 transport vessels.
You hacked 15 enemy capital ships.
You destroyed 10 enemy capital ships.
You served at a Veteran's level during the Triton mission.
You served at an Elite level during the Triton mission.
You served at an Elite level during the Neptune orbital mission.
You served at a Veteran's level during the Neptune atmosphere mission.
You served at an Elite level during the Neptune atmosphere mission.
You served at a Veteran's level during the Uranus mission.
You served at an Elite level during the Uranus mission.
You served at a Veteran's level during the Saturn mission.
You served at an Elite level during the Saturn mission.
You served at a Veteran's level during the Titan mission.
You served at an Elite level during the Titan mission.
You performed a heroic action during the Saturn mission.
You completed a mission with 75% or higher accuracy.