Here is the full list of all 24 The Initiate achievements.
Take the Front Door Key and Escape
Complete the game
Use the gun and end the trial
Find and Replace all Map Pieces
Solve the Statue Puzzle
Solve the Stained Glass Puzzle
Solve the Candle Puzzle
Find and Collect all Notes
Solve the Light Up Puzzle
Solve the Pressure Pad Puzzle
Solve the Memory Puzzle
Move the Piano
Solve the Owl Puzzle
Pull Out a Red Book
Place the water pipe and take the key
Solve the Cave Gate Puzzle
Solve the Special Object Puzzle
Find an Octagon Shaped Object
Find a Triangle Shaped Object
Solve the Card Puzzle
Find a Square Shaped Object
Solve the Book Place Puzzle
Find and Collect a Flashlight
Complete the Game Within Two Hours