If not Zelda II, then I think I would have to say either The Legend of Zelda, or A Link to the Past. Both of these games are undeniably difficult. TLoZ is difficult because of the overworld. There are no signs telling you where to go, no charters pointing you in the right direction, no nothing. Just finding all the dungeons can be a chore, and that doesn't even mention how hard it is to beat the dungeons. I find myself missing all the time when I want to hit an enemy, and that usually causes me to hear the super nostalgic game over music. The enemies are so random and unpredictable too, so there is no way to know where they are going to be. They could go from behind you to directly in front of you right under your nose.
A Link to the Past is hard because it was very puzzle focused. Each dungeon had tons of complex puzzles that I admit actually gave me trouble on my first playthrough. The puzzles are ingeniously designed, and perfect on the challenging side. Combat in ALttP, though improved since TLoz, is still quite difficult and unpredictable, and some enemies can prove to pose quite a challenge on the player if they are, like I am, inaccurate and impatient with the sword.
It is hard to decide which game, between these two, is harder. But, I think ALttP wins that trophy simply because the game made players think more. Combine the puzzles with the tough enemies, and ALttP is actually a much more difficult game than some people give it credit for.