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