Here is the full list of all 17 The Battle of Sol achievements.
Earn a Gold Medal on every mission
Earn at least a Silver Medal on every mission
Kill 7 fighters in Mission 3
Kill 3 COD Daggers in Mission 13
Destroy 10 missiles launched from the enemy Frigate
Win the shooting contest in Mission 7
Destroy 10 Frigate turrets in Mission 9
Destroy all missiles before they hit the Rising Light in Mission 19
Save all 5 Transports in Mission 14
Defeat Brother Gunel without dropping below 15% Hull Integrity in Mission 16
Don't fail a hack in Mission 21
Complete all Bonus Objectives in the Prologue Missions
Destroy a COD Dagger with a non-homing missile
Beat the single player campaign
Destroy a COD Morningstar using its own missile
Destroy 10 homing missiles while in Slide
Destroy 10 enemies using the beam weapon