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