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