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