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