Here is the full list of all 14 eversion achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Find the secret ending.
You tried to edit the main game files. You won't be able to get other achievements or high scores until you undo your edits. (custom time attack maps are ok!)
Find the special ending.
Find the hidden item on each stage. No, there's not an ending for this one.
Enter the final eversion layer.
Gather 240 gems.
Find the regular ending.
See all alternate stage start messages.
Enter the sixth eversion layer.
Enter the fifth eversion layer.
Enter the fourth eversion layer.
Enter the third eversion layer.
Enter the second eversion layer.
Enter the first eversion layer.