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