Here is the full list of all 37 Alexis Almighty: Daughter of Hercules achievements.
Use the torch 25 times to illuminate the path
Set 1000 tasks for workers!
Build 30 buildings!
Find 20 puzzle pieces
Collect 50 materials at any level
Collect 50 food at any level
Complete Chapter One
Break all the portals on the first levels
Use a skill!
Collect 500 food!
Complete 10 levels!
Complete 10 levels with 3 stars!
Complete a level without using skills!
Complete any level in Gold time without using bonuses
Find 10 puzzle pieces
Collect 100 food!
Complete Level 1!
Complete a level with 3 stars!
Find the first puzzle piece
Complete Chapter Two
Complete Chapter Three
Complete Chapter Four
Defeat all of Chronos' minions
Defeat the Magician of Chronos
Save all the inhabitants in distress
Open all the doors
Use the mana well 50 times
Use the clock 50 times
Save Odysseus
Use a skill 20 times!
Complete 30 levels with 3 stars!
Find 40 puzzle pieces
Activate the Accelerated Bonus three times at the same level
Use two bonuses simultaneously
Use all the bonuses at least once
Get all the achievements
Complete Chapter Five