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.
Build 50 missile launchers
This honorary rank is given for 30 000 killed enemies
Save the planet from the democracy lantern
Destroy Emperor's pedestal
Brew up 100 tanks
Build 20 support towers
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
Free Aludrians from 200 jellyfish
Demolish any 200 objects on the map
Kill one reanimator
Demolish armor obelisk
Collect 1 000 gold units
Destroy 10 000 enemies
Demolish health obelisk
Stop Phoenix
Build any 500 towers
Destroy 5 Aludrian mines
Kill 500 doctors
Collect 50 000 silver units
Build 80 factories
Crash 100 destroyers
Kill 300 spiders
Build a support tower
Destroy any 50 objects on the map
Kill 100 doctors
Collect 200 gold units
Abolish any 10 objects on the map
Collect 20 000 silver
Send to the skies 2 000 enemies
Kill 300 scouts
Send to the skies 150 Aludrian officers
Destroy the destroyer
Raze the fallen missile to the ground
Build any 50 towers
Kill 1 000 enemies.
Kill 150 troopers
Build ten energy towers
Kill the first Aludrian!
Build three factories
Build one energy tower
Build two machine-gun towers
Kill the first attacking Hamalian!