Here is the full list of all 48 Chaos Galaxy achievements.
Mercenary factions random trigger event
Aerie Assassins random trigger event
Pirate factions random trigger event
Trader factions random trigger event
Omnic factions random trigger event
Imperial fleets random trigger event
Black Khalif Jihad random triggers event
Imperial vassals random trigger event when the Imperial Court is not in a state of war
Imperial allies random trigger event when the Imperial Court is not in a state of war
Imperial vassals and allies random trigger event when the Imperial Court is not in a state of war
Random trigger event when faction has assassins or ninjas
Trigger event when Omnic Apocalypse destory Mozi Order
Trigger event when Southsea Guild destory Eastgalaxy Corp.
Trigger event when Eastgalaxy Corp. destory Southsea Guild
After G.E.1/1021, random trigger event when Southeaven Fleet is a vassal of Imperial Court
After G.E.1/1022, random trigger event by Imperial Court
Trigger event when Regent Forces destory Royalist Alliance
Trigger event when Royalist Alliance destory Regent Forces
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Northsky Fleet
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Eastocean Fleet
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Southeaven Fleet
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Westwastes Fleet
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Southsea Guild
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Eastgalaxy Corp.
Trigger event when Shendu captured by Emishi Pirates
Trigger event when Shendu captured by Kurushima Pirates
Trigger event when Shendu captured by Pella Corps
Trigger event when Shendu captured by Lycurgus Corps
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Aerie Assassins
Trigger event when Shendu captured by Black Khalif Jihad
Before the great civil war breaks out or other factions captured Shendu, trigger event when Shendu captured by Mozi Order
Trigger event when Shendu captured by Omnic Apocalypse
Using Galaxy Empire to complete the game
Using Northsky Fleet to complete the game
Using Eastocean Fleet to complete the game
Using Southeaven Fleet to complete the game
Using Westwastes Fleet to complete the game
Using Southsea Guild to complete the game
Using Eastgalaxy Corp. to complete the game
Using Emishi Pirates to complete the game
Using Kurushima Pirates to complete the game
Using Pella Corps to complete the game
Using Lycurgus Corps to complete the game
Using Aerie Assassins to complete the game
Using Black Khalif Jihad to complete the game
Using Mozi Order to complete the game
Using Omnic Apocalypse to complete the game
Using a vassal faction to complete the game