Here is the full list of all 44 Destroy The Monoliths achievements.
Complete the tutorial
Win a mission with 2 monoliths to destroy
Win a mission with 3 monoliths to destroy
Win a mission with 4 monoliths to destroy
Win a mission with 5 monoliths to destroy
Cleanse an entire world
Discover 8 different biomes
Freeze and upgrade 100 blocks
Open 50 treasures
Relocate the Core 20 times
Use a shrine 35 times
Reroll new technology choices 20 times
Kill 10 minions with magma traps
Win a mission without killing a minion by yourself
Place more than 100 buildings during a mission
Repair fully the Core after it had less than 100 health points remaining
Kill a titan minion using a death shrine
Destroy manually more than 500 buildings
Mine more than 400 blocks during a mission
Unlock the Main offensive technology #2
Unlock the Main offensive technology #3
Unlock the Main offensive technology #4
Unlock the Starting technologies pack #2
Unlock the Starting technologies pack #3
Unlock the Starting technologies pack #4
Unlock the Starting technologies pack #5
Unlock the Doomed relic #1
Unlock the Doomed relic #2
Unlock the Doomed relic #3
Unlock the Doomed relic #4
Unlock the Doomed relic #5
Cleanse an entire world with 1 Doomed relic activated
Cleanse an entire world with 2 Doomed relics activated
Cleanse an entire world with 3 Doomed relics activated
Cleanse an entire world with 4 Doomed relics activated
Cleanse an entire world with 5 Doomed relics activated
Fall into the void
Win a mission after the Core is destroyed
Reroll a new world name 50 times
Get killed by a minion hidden in a trapped chest
Push an elite minion into the void
Defeat the Colossus
Unlock the Starting technologies pack #6
Finish to destroy a monolith by yourself