Here is the full list of all 53 SOL: Exodus achievements.
You downed 20 COD fighters.
You successfully completed the Pluto mission.
You served at a Veteran's 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 survived the UCS-1 mission.
You served at a Veteran's level during the UCS-1 mission.
You completed a mission with 75% or higher accuracy.
You completed a mission using only guns.
You downed 100 COD fighters.
You downed 250 COD fighters.
You protected 10 transport vessels.
You protected 25 transport vessels.
You destroyed 10 ADP's.
You destroyed 15 ADP's.
You destroyed 20 ADP's.
You hacked 10 enemy capital ships.
You hacked 15 enemy capital ships.
You destroyed an enemy capital ship.
You destroyed 5 enemy capital ships.
You destroyed 10 enemy capital ships.
You took out an enemy missile.
You took out 25 enemy missiles.
You took out 50 enemy missiles.
You successfully completed the Triton mission.
You successfully completed the Neptune orbital mission.
You successfully completed the Neptune atmosphere mission.
You successfully completed the Uranus mission.
You successfully completed the Saturn mission.
You successfully completed the Titan mission.
You served at an Elite level during the UCS-1 mission.
You served at an Elite level during the Pluto mission.
You served at a Veteran's level during the Triton mission.
You served at an Elite level during the Triton mission.
You served at a Veteran's level during the Neptune orbital 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 UCS-1 mission.
You performed a heroic action during the Triton mission.
You performed a heroic action during the Neptune orbital mission.
You performed a heroic action during the Neptune atmosphere mission.
You performed a heroic action during the Uranus mission.
You performed a heroic action during the Saturn mission.
You performed a heroic action during the Titan mission.