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