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