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