I would say that the final battles with Dr. Wiley at the ends of Mega Man 7 and Mega Man 8 were the most difficult moment in the classic series! (There's a reason as to why Wiley has such a wicked grin in those battles! Come to think of it, the final fight with Dr. Wiley in Mega Man II was difficult as well!) However, the rest of those Mega Man games leading up to that point weren't especially difficult.
Overall and as a whole, I'm actually going to all the way back to the original Mega Man as the most difficult of the classic series! Not only does it have especially aggravating moments like the platforming in Gutsman's stage or the fight with the Mega Man clone, but we're talking about the game that doesn't even have a password system! Cheating or not, the pause trick with Electric Beam and the Cut Blade is an absolute godsend!