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.
Destroy your ship 10 times.
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.
Destroy your ship 7 times.
Finish level 19.
Destroy ship type 2675 Tolkien.
Destroy your ship 5 times.
Finish level 18.
Finish level 17.
Finish level 16.
Finish level 15.
Destroy your ship 3 times.
Destroy ship type 99942 Apophis.
Finish level 14.
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.
Finish level 12.
Destroy ship type 912 Maritima.
Destroy missile type 18 Melpomene.
Spend 50 system upgrade points.
Spend 5 ship upgrade points.
Reach player level 50.
Reach player level 45.
Finish level 11.
Destroy ship type 9165 Raup.
Destroy ship type 192 Nausikaa.
Use holodrones 29 times.
Spend 40 system upgrade points.
Spend 4 ship upgrade points.
Finish level 10.
Kill Rigil.
Reach player level 40.
Use fast repair 34 times.
Spend 30 system upgrade points.
Spend 3 ship upgrade points.
Reach player level 35.
Finish level 9.
Reach player level 30.
Destroy your ship.
Use holodrones 23 times.
Reach player level 25.
Finish level 8.
Use fast repair 21 times.
Destroy 500 enemy ships.
Use holodrones 17 times.
Destroy 250 asteroids.
Destroy 50 enemy waves.
Destroy missile type 15 Eunomia.
Spend 20 system upgrade points.
Spend 2 ship upgrade points.
Reach player level 20.
Finish level 7.
Use fast repair 13 times.
Destroy ship type 433 Eros.
Use holodrones 11 times.
Destroy 250 enemy ships.
Use fast repair 8 times.
Reach player level 15.
Finish level 6.
Destroy ship type 846 Lipperta.
Use holodrones 7 times.
Use fast repair 5 times.
Destroy 100 asteroids.
Shoot 250 rockets.
Spend 10 system upgrade points.
Spend ship upgrade point.
Reach player level 10.
Finish level 5.
Use holodrones 3 times.
Use fast repair 3 times.
Destroy 25 enemy waves.
Use fast repair 2 times.
Destroy 100 enemy ships.
Use holodrones.
Use fast repair.
Finish level 4.
Destroy 50 asteroids.
Finish level 3.
Reach player level 5.
Destroy 50 enemy ships.
Destroy ship type 2000 YY.
Shoot 1000 plasma bullets.
Shoot 100 rockets.
Destroy 25 asteroids.
Spend system upgrade point.
Finish level 2.
Shoot 500 plasma bullets.
Destroy 10 enemy waves.
Destroy ship type 1999 XC.
Shoot 1000 bullets.
Finish level 1.
Shoot 50 rockets.
Destroy 10 asteroids.
Destroy 10 enemy ships.
Shoot 250 plasma bullets.
Shoot 500 bullets.
Destroy asteroid.
Destroy ship type 7 Iris.
Shoot 25 rockets.
Shoot 250 bullets.
Level up!
Finish tutorial level.
Destroy enemy wave.
Destroy enemy ship.
Destroy ship type 288 Glauke.
Shoot 100 plasma bullets.
Shoot 100 bullets.
Shoot 50 plasma bullets.
Shoot 25 plasma bullets.
Shoot 10 rockets.
Shoot 10 plasma bullets.
Shoot 50 bullets.
Shoot 25 bullets.
Shoot 10 bullets.
Shoot one rocket.
Shoot bullet.
Shoot plasma bullet.