Here are ALL 12 achievements in the game and what needs to be done to get them.

Traversed World 2 (10)
Travel ALL the way across World 2.

Traversed World 3 (10)
Travel ALL the way across World 3.

Traversed World 4 (10)
Travel ALL the way across World 4.

Traversed World 5 (10)
Travel ALL the way across World 5.

Traversed World 6 (10)
Travel ALL the way across World 6.

Solved World 2 (15)
Fit together ALL the world 2 puzzle pieces and align the puzzle in it's frame.

Solved World 3 (15)
Fit together ALL the world 3 puzzle pieces and align the puzzle in it's frame.

Solved World 4 (15)
Fit together ALL the world 4 puzzle pieces and align the puzzle in it's frame.

Solved World 5 (15)
Fit together ALL the world 5 puzzle pieces and align the puzzle in it's frame.

Solved World 6 (15)
Fit together aLL the world 6 puzzle pieces and align the puzzle in it's frame.

Speed Run (15)
Complete a full speed run of the entire game beating the challenge time.

Closure (60)
Complete the game.

To be able to reach the door in the attic that allows you to enter World 1 you must first repair the ladder in the house (level select area). This is done by finding ALL 72 puzzle pieces and assembling each world's jigsaw puzzle. When you have beaten World 1 you will be taken directly to the Epilogue which you can return after beating it any time you want by walking into an offscreen alcove which is reached by going left at the 'Title' screen.

When you have collected ALL 7 of the secret stars an 8th star will be available in the final level and some of the switches will become immune to time manipulation allowing you to reach the 8th star and change the ending of the game.

When you reach the second-to-last room just before the castle in the Epilogue jump from the elevated platform onto the middle of the bridge (rock) and if you perform the move correctly you will hear a confirmation sound and a new journal entry will appear.