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