Here is the full list of all 34 StarDrive 2 achievements.
Start a game with an empire named "United Federation"
Start a new game with a leader named Honor Harrington
Start a game with a leader name containing "Skywalker"
Start a game with a leader name containing "Picard"
Start a game as the Kulrathi, with an empire name containing "Kilrathi" or "Bulrathi"
Start a game with a race named after one of the races found in the Galactic Civilizations games
Start a game with an empire named after one of the races found in the Master of Orion games
Start a game with a leader name containing "Adama"
Start a game ith an empire named after one of the races found in Endless Space
Colonize a Gaia planet
Colonize an asteroid belt
BUT IT RAINS DIAMONDS. Colonize a world with the Diamond Rain special
Own a colony that has reached its population limit while being populated entirely by androids
Use transports to move 10+ citizens (across any number of games) from one colony to another
Unleash the plague bomb on a planet
Have four or more citizens living on a single asteroid belt
Conquer Earth with a ground invasion
Capture a planet while possessing the powers of assimilation
Sacrifice a citizen from another race
Sacrifice one of your own citizens
Conduct a foreign exchange
Travel through a wormhole for the first time
Control 8 or more colonies
Have a fleet run out of fuel in deep space
Control enough sources of Spice to gain the exploitation bonus
Use espionage to plant a mole in another empire
Win the game using a custom race that has no positive traits and at least -8 negative trait picks
Have a salvo of at least 100 missiles in flight at a single time in a battle launched from the strategy map
Have at least 50 fighters deployed at the same time in a battle launched from the strategy map
Win a ground combat as a race with the Timid trait
Eliminate a planetary population through orbital bombardment
Successfully lift another species to sentience
Have a single ship intercept and destroy at least 100 missiles in a single battle
Successfully threaten a race into giving you something they wouldn't have otherwise given you