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