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