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