Here is the full list of all 20 Loop achievements.
Meeting The Mentor
A New Cycle Begins
The Search For Order
The Reign Of Chaos
A Step Forward
The Old Ways Of Liberation
Chaos Intervenes
Meeting The Young Spirit
The Cycle Repeats
Restoring The Unbreakable
Mastering The Truth
Facing Chaos
Accepting Order And Chaos
Breaking The Loop
The Warning
Facing The Unknown
Find your master's master mask
Place the two boxes in the furthest mold
Do the second tower in reverse
Press a button too many times