Here is the full list of all 20 Hexa Turn achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Turn 1000 Hexagons
Unlock all levels of package 4
Complete all levels of pack 4
Solve 96 levels without using bonus.
Turn 500 Hexagons
Solve 75 levels without using bonus.
Unlock all levels of package 3
Complete all levels of pack 3
Solve 50 levels without using bonus.
Unlock all levels of package 2
Complete all levels of pack 2
Turn 250 Hexagons
Spell "Hexa Turn"
Unlock all levels of package 1
Complete all levels of pack 1
Solve 25 levels without using bonus.
Turn 100 Hexagons
Solve 10 levels without using bonus.
Turn 50 Hexagons
Turn 25 Hexagons