Hard puzzles are available in the Gallery after they are completed.
I will make this more clear in the "Intro" section of the guide.

I only see "easy" and "normal" when I play the game. How do I unlock hard mode? I've beaten around the first 11 levels or so all on "normal." The only achievements left are timed achievements, repeat achievements, and hard level achievements. I just don't know how to get to the "hard" levels.