You will get this achievement for completing the Campaign mode.
There are three Chapters, each has five missions:
Tower - Great Ziggurat
I - Foundations - Kill 75 Workers
II - Fire And Brimstone - Withstand 20 Waves of Workers
III - False Prophets - Defeat 40 Priests
IV - Deluge - Resist for 8 Minutes
V - Wind of Change - Kill 450 Workers
Tower - Tower of Babel
VI - A New Beginning - Fight Off The Workers for 9 Minutes
VII - Cursed Path - Spare 25 Cursed Jars
VIII - Rosary of Souls - Score 100,000 Points
IX - Sea Legs - Destroy 72 Ships
X - Under Siege - Destroy 30 Construction Towers
Tower - Hanging Gardens
XI - Divine Gardens - Kill 450 Workers
XII - Accursed Priests - Withstand 42 Waves of Workers
XIII - Babel Towers - Destroy 5 Construction Towers, Then 25 Priests
XIV - Soul Collector - Score 500,000 Points
XV - Last Stand - Resist for 20 Minutes
I had trouble with points missions. When you are doing them you should focus on getting high multipliers by swapping attacks over and over. I managed to get a 20x multiplier at the first time on the mission 14, then about 62x at the second time, and this brought me victory. Make sure you are using combination spirit, it extends the time during which you can continue the sequence after connecting one of the forces to the chain, it's a huge help towards your goal.
Thanks to Elyoh for the names of the missions, I have them in Russian.