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