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