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