No segments of Skyward Sword were really that much more difficult to complete than others, as the game was pretty well-balanced. But if I had to choose any specific part of the game that stumped me a bit longer than usual, one of the top contenders would have to be the somewhat perplexing puzzle before Link is able to enter the Isle of Songs for the first time. The problem was that it takes some trial and error to understand what exactly it is that the player needs to do, as the three-piece puzzle board and the large statues placed in random places in a circle doesn't clearly indicate what needs to be done.
The puzzle probably took around ten minutes or so, but I still thinks it's harder than the major puzzles in Twilight Princess. While I enjoyed the ice blocks and the Master Sword puzzle, both took me far less than ten minutes in my last playthrough. It's sort of a shame that more brain-teasers like these weren't included in the game, but in the very first minutes of the Ancient Cistern, Link is confronted with the glaring challenge of figuring out the combination for the lock on the door. The solution to this problem was quite obvious in the Sandship, but the hints in the Ancient Cistern are very subtle.
A stone slab gives the player a pretty major hint, but a lot of gamers will either not notice it or dismiss the hints it gives you as part of a later section of the game. Nope! Symbols appear on the large statue in the center of the room, and reading and memorizing the order of these symbols is what allows the player to progress. I struggled with this to the point where I just checked Zelda Dungeon's walkthrough for the combination and moved on without straining my brain further.