Dr. Robotnik, Mean Bean Machine. Unless you're a real buff for puzzle games of the "drop blocks into a pit" variety, you'll get raped repeatedly just trying to get to him, let alone beat him.
Seconding Spinball's final boss, moreso because it's really irritating than it is capable of actually killing you. Screw up a difficult shot three times and you're sent halfway back down the level again. As mentioned, just getting up there is a challenge in itself, and there's the risk of having to do he majority of it all over again if you hit those windsocks too much.
The second fight with King Arthur in Black Knight is notable, but at least beatable. Lancelot Returns, on the other hand, just displays how much of an asshole Shadow can really be when he's not pulling punches, mostly in the form of projectile and Chaos Blast spam, and the reflexes of a goddamned robot. And the sword-clash moments? **** them to hell, I've never been able to win one even once and to this day I still don't know the trick to it.
Sonic 2's final boss, not the game gear one. This is actually somewhat easy (hell, even boring) once you have the pattern figured out, but expect to lose dozens of lives learning it the hard way. The fact that it's one of relatively few bosses that expect you to win with no rings just adds to the trouble.
Dark Gaia, oh for the love of god Dark Gaia. Again, the difficulty is mostly fake. It's bad enough that we had to endure the Mighty Morphin' Power Rangers shtick, but slowly advancing through gigantic fireballs with such slugglish controls is more difficult than it sounds, and then every now and then Gaia just thows a high-damage near-undodgeable beam at you just to be a pain in the tits. Then we have QTE sequences in lieu of the two punch buttons designed specifically for this boss fight, and a hectic run through a brief Sonic section loaded with trial and error deaths and a super-strict invisible timer. Rinse and repeat two or three times and that's Dark Gaia for you.
The last two bosses of Secret Rings I recall being pretty hard, but for what reasons I can't remember right now. Just that landing the close range smackdown with Darkspines is absolutely awesome and easily makes up for whatever difficulty it throws at you.