Here is the full list of all 128 Duke of Alpha Centauri achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Survive 5 minutes in endless mode.
Survive 4 minutes in endless mode.
Survive 3 minutes in endless mode.
Survive 2 minutes in endless mode.
Survive one minute in endless mode.
Destroy your ship 10 times.
Play endless level.
Finish level 20.
Finish all levels on any difficulty.
Kill Proxima.
Finish level 19.
Destroy ship type 2675 Tolkien.
Finish level 18.
Spend 6 ship upgrade points.
Finish level 17.
Destroy your ship 7 times.
Finish level 16.
Finish level 15.
Destroy ship type 99942 Apophis.
Spend 5 ship upgrade points.
Finish level 14.
Destroy your ship 5 times.
Destroy ship type 1235 Schorria.
Spend 50 system upgrade points.
Reach player level 50.
Finish level 13.
Destroy ship type 4524 Barklajdetolli.
Destroy ship type 1036 Ganymed.
Spend 4 ship upgrade points.
Reach player level 45.
Finish level 12.
Destroy ship type 912 Maritima.
Destroy missile type 18 Melpomene.
Spend 40 system upgrade points.
Spend 3 ship upgrade points.
Finish level 11.
Reach player level 40.
Destroy ship type 9165 Raup.
Reach player level 35.
Destroy your ship 3 times.
Destroy ship type 192 Nausikaa.
Finish level 10.
Kill Rigil.
Spend 30 system upgrade points.
Reach player level 30.
Finish level 9.
Use fast repair 34 times.
Spend 2 ship upgrade points.
Reach player level 25.
Use holodrones 29 times.
Destroy 100 enemy waves.
Spend 20 system upgrade points.
Spend ship upgrade point.
Spend 10 system upgrade points.
Reach player level 20.
Use holodrones 23 times.
Reach player level 15.
Destroy your ship.
Use fast repair 21 times.
Destroy 250 asteroids.
Finish level 5.
Use holodrones 17 times.
Reach player level 10.
Finish level 8.
Use fast repair 13 times.
Destroy 500 enemy ships.
Use holodrones 11 times.
Destroy 50 enemy waves.
Destroy missile type 15 Eunomia.
Use fast repair 8 times.
Reach player level 5.
Finish level 7.
Destroy 100 asteroids.
Shoot 250 rockets.
Shoot 1000 plasma bullets.
Destroy ship type 433 Eros.
Use fast repair 5 times.
Use holodrones 7 times.
Destroy 250 enemy ships.
Finish level 6.
Destroy ship type 846 Lipperta.
Use fast repair 3 times.
Use fast repair 2 times.
Destroy 50 asteroids.
Use fast repair.
Shoot 500 plasma bullets.
Use holodrones 3 times.
Shoot 100 rockets.
Shoot 1000 bullets.
Destroy 25 asteroids.
Destroy 25 enemy waves.
Destroy 100 enemy ships.
Finish level 4.
Use holodrones.
Shoot 250 plasma bullets.
Destroy 10 asteroids.
Shoot 500 bullets.
Spend system upgrade point.
Finish level 3.
Level up!
Shoot 50 rockets.
Destroy 50 enemy ships.
Destroy ship type 2000 YY.
Shoot 250 bullets.
Finish level 2.
Shoot 100 plasma bullets.
Destroy 10 enemy waves.
Shoot 25 rockets.
Destroy ship type 1999 XC.
Shoot 50 plasma bullets.
Finish level 1.
Destroy asteroid.
Destroy 10 enemy ships.
Shoot 100 bullets.
Shoot 25 plasma bullets.
Shoot 10 plasma bullets.
Shoot plasma bullet.
Destroy ship type 7 Iris.
Finish tutorial level.
Destroy enemy wave.
Destroy enemy ship.
Destroy ship type 288 Glauke.
Shoot 10 rockets.
Shoot 50 bullets.
Shoot 25 bullets.
Shoot 10 bullets.
Shoot one rocket.
Shoot bullet.