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