Here is the full list of all 102 Master of Orion achievements.
Successful trade with another Race for the first time
Develop a Colony that yields 20 Food Points per turn
Command and win your first Tactical Battle
Colonize your first planet
Colonize the first planet your Colony Ship visits in a match
Destroy 15 Pirate ships
Discover 3 Anomalies and Bombard 2 Pirate bases in a match
Build 2 Marine Barracks
Build your first Spy Center
Research 8 Technologies before turn 50
Reach 15 Population Units before turn 35
Block all warp points to your home planet before turn 20
Declare War for the first time
Defeat Orion's Guardian before turn 150
Visit all systems in the galaxy during a match
Win a match in less than 100 turns
Spy on the Humans as a Psilon
Successfully Incite Revolt on a Darlok Colony
Build 10 Asteroid mines inside your empire
Have 2 planets fully populated
Build 20 Ships before turn 100
Don’t have strikes in any of your colonies for 80 turns
Successfully gather information on 5 Colonies in a match via espionage
Colonize a planet in each possible biome in a match
Engage in combat using a fleet of 20 or more ships
Incite Revolt in 3 different opponents' colonies
Deport 5 spies
Kill 5 spies
Use at least 15 Civilian Transports in a match
Buy 30 ships in a match
Colonize every planet in 5 systems
Eliminate all Space Monsters in a match
Eliminate the Alkari first while playing as Mrrshan
Win a multiplayer match
Destroy 20 planets with a Doomstar in a match
Win by Conquest without losing a single colony
Have at least 1 colony on 20 different stars
Spy on all races during a match
Completely research the Tech Tree and win by Conquest
Destroy an opponent's Homeworld using the Doomstar
Colonize at least 5 Oceanic planets in a match
Colonize at least 5 Volcanic planets in a match
Colonize at least 5 Desert planets in a match
Invade 10 colonies in a match
Win by Economic Victory with the Alkari
Win by Technological Victory with the Bulrathi
Win by Military Victory with the Darlok
Win by Economic Victory with Humans
Win by Economic Victory with Klackon
Win by Diplomatic Victory with Meklar
Win by Technological Victory with Mrrshan
Win by Economic victory with Psilon
Win by Diplomatic Victory with Sakkra
Win by Diplomatic Victory with Silicoid
Win by Technological Victory with Sakkra
Win by any victory with only 5 planets colonized including your homeworld
Use your Jump Gates 100 times during a match
Complete the entire tech tree for the first time
Have 7 spies on 7 different races
Build 15 Jumpgates in a match
Win by Economic Victory with 80% or more of the outstanding GMF Shares.
Have a colony with at least 1 Population Unit of another race in a match
Get your capital planet blown up in a super nova
Convert 10 Asteroid Fields / Gas Giants into Inhabitable Planets
Ally with all Races
Have a fleet that costs more than 30 Command Points
Win the game without building a single military ship
Have a Colony yielding 70 Research Points
Rename 100 Blueprints
Invade 100 planets
Destroy 5000 ships
Destroy 100 Planets
Establish 100 colonies
Scrap 600 Blueprints
Buy 1000 structures or ships
Break 150 pacts
Watch the credits in full
Turn 20 planets into Inferno
Turn 20 planets into Tropical
Turn 20 planets into Cavernous
Turn 20 planets into Grassland
Play 1000 turns
Play 5000 turns
Play 10000 turns
Win by all Victory types with any race
Win by Excellence Victory for the first time
Win by Conquest Victory for the first time
Win by Technological Victory for the first time
Win by Economic Victory for the first time
Win by Diplomatic Victory for the first time
Win all victory types with the Alkari
Win all victory types with the Bulrathi
Win all victory types with the Darlok
Win all victory types with the Human
Win all victory types with the Klackon
Win all victory types with the Meklar
Win all victory types with the Mrrshan
Win all victory types with the Psilon
Win all victory types with all races
Win the game with all races at least once in Hard difficulty
Win all victory types with the Sakkra
Win all victory types with the Silicoid