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