Here is the full list of all 51 Eternal Space Battles achievements.
Destroy 100 enemies in one run
Destroy 300 enemies in one run
Destroy 500 enemies in one run
Destroy 700 enemies in one run
Destroy 1000 enemies in one run
Unlock all upgrades for spaceship N1
Unlock all upgrades for spaceship N2
Unlock all upgrades for spaceship N3
Unlock all upgrades for all spaceships
Unlock spaceship N2
Unlock spaceship N3
Defeat the first boss
Defeat the second boss
Defeat the third boss
Defeat the second boss using the spaceship N1
Defeat the third boss using the spaceship N2
Defeat the third boss using the spaceship N1
Dodge the enemy shrapnel
Avoid destruction using the "Phoenix"system
Complete 5 missions
Complete 10 missions
Complete 20 missions
Use the "Destroyer" 5 times in one flight
Use the "Destroyer" 10 times in one flight
Use the "Destroyer" 15 times in one flight
Destroy 25 enemies by ramming them
Destroy 50 enemies by ramming them
Destroy 75 enemies by ramming them
Destroy 100 enemies by ramming them
Destroy 200 enemies by ramming them
Destroy the barrier before the enemy
Fail in a boss battle
Defeat the first boss using the spaceship N1 in 40 seconds
Defeat the second boss using the spaceship N2 in 40 seconds
Defeat the third boss using the spaceship N3 in 50 seconds
Increase enemy level by 2 in one fight
Increase enemy level by 4 in one fight
Increase enemy level by 6 in one fight
Get special weapons level 3
Trigger all amplifiers simultaneously
Set your first result
Save 1000 credits
Save 2000 credits
Save 5000 credits
Save 10000 credits
Save 20000 credits
Be destroyed 5 times
Be destroyed 10 times
Be destroyed 25 times
Be destroyed 50 times
Be destroyed 100 times