Relatively normal achievements
We will not retreat! - When your
home system is your only system left, destroy it while you are at war. (you should save your game first

)
That was close! - While at war, all your systems (except for your
home system!) get completely destroyed or conquered. Then, the war ends (no matter how).
That would have been good to know EARLIER - Your empire gets reduced to one system (not necessarily home system). Then, you find an ancient spaceship.
Freeing the slaves - Reconquer a planet that was formerly taken away from you by another empire.
Freezing the slaves - Conquer an enemy species' planet. Then, you put the population on an arctic planet without infrastructure.
Now, we are the first ones - Create a new species and settle it on a planet.
We have your capital, now surrender! - Conquer the homeworld of another empire.
Hello, we are your new neighbours - Colonise a planet in the home system of another empire or species.
Federation of United People - Be part of a federation that includes every empire in the galaxy (except for rebels and pre-FTL species).
No Galactic Peace - Be part of a federation that included every empire in the galaxy (except for rebels and pre-FTL species), until it dissolved completely.
Pre-FTL species achievements
I am good at exploration - Discover five other species within one year, not including variations of the same species.
Obey the Prime Directive! - A pre-FTL species (that only you know of) gets destroyed by an event and you don't do anything to help / preserve the species.
Screw the Prime Directive! - A pre-FTL species was going to be destroyed by an event. You either prevented the event or evacuated the population.
You! Stay! There! - Keep a pre-FTL species that achieved FTL travel from leaving their home system. Do this for ten years.
You were uplifted. Now you are enslaved. - Uplift a pre-FTL species only to conquer them after that.
That was not intended, not yet - A ship or fleet of your empire gets transferred to another star system by an event. In that system, you make contact with a fallen empire.
Cannibalistic and underdeveloped - A pre-FTL species with a cannibalistic society eats the people you previously sent on their planet to make contact.
Unexpectedly fast evolution - Find a former pre-FTL species that has achieved space travel on their own.
You are not worthy - Destroy a pre-FTL species.
We knew you would come - A pre-FTL species that just achieved space travel (because of you???) finds a way into a system controlled by you.
Do NOT kill yourselves! - Prevent a pre-FTL species from killing themselves in a nuclear war.
Do not kill my friends! - Destroy or enslave another empire, that was at war with a pre-FTL species you knew, when your war against them began.
You will be assimilated!
We are Borg - Turn the whole population of your empire into cyborgs.
Assimilation - Conquer another empire and turn them into cyborgs, while your whole population consists of cyborgs.
Technological Distinctiveness - Board a spaceship of another empire while you are a cyborg empire.
Fallen empires, new species, ancient artifacts
Frozen Forerunners - Find ruins of a fallen empire on an arctic world.
Cities of the ancients - Conquer a planet of a fallen empire.
You are not my father! - Destroy a fallen empire completely.
Mighty friends - Get a fallen empire to ally with you.
Mighty allies - Get a fallen empire to join a federation with you.
Robots have no rights - An AI species comes to existence. Then, you enslave it.
Created for one purpose - Genetically engineer a pre-sentient species and then integrate them into your empire
We just visited... - Genetically engineer a pre-sentient species and leave it alone then.
Conspiracy theories are true! - Find an alien ruin on a planet in your home system and investigate it.