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