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