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.
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.
Destroy your ship 10 times.
Finish level 17.
Finish level 16.
Finish level 15.
Destroy ship type 99942 Apophis.
Destroy your ship 7 times.
Finish level 14.
Destroy your ship 5 times.
Destroy ship type 1235 Schorria.
Spend 6 ship upgrade points.
Finish level 13.
Destroy ship type 4524 Barklajdetolli.
Destroy ship type 1036 Ganymed.
Destroy 100 enemy waves.
Spend 5 ship upgrade points.
Spend 50 system upgrade points.
Finish level 12.
Reach player level 50.
Destroy ship type 912 Maritima.
Destroy missile type 18 Melpomene.
Reach player level 45.
Finish level 11.
Destroy ship type 9165 Raup.
Destroy ship type 192 Nausikaa.
Spend 40 system upgrade points.
Reach player level 40.
Finish level 10.
Kill Rigil.
Spend 3 ship upgrade points.
Spend 4 ship upgrade points.
Spend 30 system upgrade points.
Finish level 9.
Use holodrones 29 times.
Reach player level 35.
Use fast repair 34 times.
Reach player level 30.
Finish level 8.
Destroy 250 asteroids.
Destroy 500 enemy ships.
Use holodrones 23 times.
Destroy 50 enemy waves.
Destroy missile type 15 Eunomia.
Spend 2 ship upgrade points.
Spend ship upgrade point.
Spend 20 system upgrade points.
Spend 10 system upgrade points.
Reach player level 25.
Finish level 7.
Shoot 250 rockets.
Use fast repair 21 times.
Use holodrones 17 times.
Destroy ship type 433 Eros.
Destroy your ship 3 times.
Destroy 250 enemy ships.
Reach player level 20.
Finish level 6.
Destroy ship type 846 Lipperta.
Reach player level 15.
Use fast repair 13 times.
Destroy 100 asteroids.
Use holodrones 11 times.
Use fast repair 8 times.
Reach player level 10.
Finish level 5.
Destroy 25 enemy waves.
Destroy 50 asteroids.
Destroy 100 enemy ships.
Use fast repair 5 times.
Finish level 4.
Use holodrones 7 times.
Shoot 100 rockets.
Use fast repair 3 times.
Spend system upgrade point.
Reach player level 5.
Finish level 3.
Destroy 50 enemy ships.
Destroy 25 asteroids.
Use fast repair 2 times.
Destroy ship type 2000 YY.
Shoot 1000 plasma bullets.
Use fast repair.
Finish level 2.
Use holodrones 3 times.
Shoot 50 rockets.
Destroy 10 asteroids.
Destroy 10 enemy waves.
Shoot 500 plasma bullets.
Destroy ship type 1999 XC.
Shoot 1000 bullets.
Finish level 1.
Shoot 25 rockets.
Shoot 250 plasma bullets.
Shoot 500 bullets.
Destroy 10 enemy ships.
Destroy asteroid.
Destroy ship type 7 Iris.
Shoot 100 plasma bullets.
Shoot 250 bullets.
Level up!
Finish tutorial level.
Destroy enemy wave.
Destroy enemy ship.
Destroy ship type 288 Glauke.
Use holodrones.
Shoot 10 rockets.
Shoot 50 plasma bullets.
Shoot 25 plasma bullets.
Shoot 10 plasma bullets.
Shoot 100 bullets.
Shoot plasma bullet.
Shoot 50 bullets.
Shoot 25 bullets.
Shoot 10 bullets.
Shoot one rocket.
Destroy your ship.
Shoot bullet.