I can also do the masonry puzzle thing, the mining/gem smash game, and the post delivery memory game on hard. I can't do the smithing thing on hard, and I can't do the fishing game at all, even on normal. I honestly haven't tried farming on hard yet, because I don't need more vegetables, and Horace's affinity hasn't been added yet.
I can also do the ballista game on hard, but why would I when it rewards the same one diamond as the normal version, but 30 gold instead of 15. As if I needed gold at that point of the game.