Here is the full list of all 47 Ancient Planet achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Save the planet from the democracy lantern
Destroy Emperor's pedestal
Build 50 missile launchers
Brew up 100 tanks
Demolish speed obelisk
Shoot down 150 storm troopers
Shoot down 10 storm troopers
Demolish attack obelisk
Stop the incubator
Save the planet from 20 reanimators
Collect 50 000 silver units
Free Aludrians from 200 jellyfish
Kill one reanimator
Demolish armor obelisk
This honorary rank is given for 30 000 killed enemies
Demolish health obelisk
Stop Phoenix
Demolish any 200 objects on the map
Destroy 5 Aludrian mines
Kill 500 doctors
Collect 1 000 gold units
Build 20 support towers
Kill 300 spiders
Build a support tower
Build 80 factories
Destroy 10 000 enemies
Destroy any 50 objects on the map
Collect 20 000 silver
Crash 100 destroyers
Build any 500 towers
Kill 100 doctors
Abolish any 10 objects on the map
Collect 200 gold units
Destroy the destroyer
Raze the fallen missile to the ground
Send to the skies 2 000 enemies
Send to the skies 150 Aludrian officers
Kill 300 scouts
Kill 1 000 enemies.
Kill 150 troopers
Build any 50 towers
Build ten energy towers
Kill the first Aludrian!
Build three factories
Build one energy tower
Kill the first attacking Hamalian!
Build two machine-gun towers