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