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