Mine is a tie.
-HG/SS Red fight. You get to the top of mount silver, and there he is. Red. The atmosphere, music, and challenge of the battle all add up to one of the greatest bosses of all time IMO.
-Xbox/Ps3 Sonic Generations Shadow Rival Battle. Instead of SA2, where one had an advantage over the other, instead, this is a battle of equals. You can both jump, spin dash, boost, etc. It's just a great boss fight in general. Way better than the 3ds fight we got.

For me it'd have to be Fume Knight from Dark Souls 2. The whole fight is practically just you trying to get a break from his powerful moveset which hardly ever leaves him open. Then comes a phase change in which he does even MORE damage and if you're not prepared for will almost certainly just walk over you.

It's really hard to decide, but I'll throw out three that immediately come to mind.

-Yami from ÅŒkami. At the start of the fight, he drains all your abilities. You basically start with nothing and, as the fight goes on, slowly regain your powers. And no power is useless here; even the skill that makes it night summons freaking Nagi with his sword! Just when it looks like you're about to lose, all the people you've helped give you your full power through the power of friendship. And then you proceed to beat that stupid fish into. The. Ground.

-Kaos from the original Skylanders. A very odd choice, but this is mainly because of the memories. My cousin and I brought both our Skylanders collections together to beat him and it was awesome. There was even a hydra we had to beat up.

-Babel from Devil Survivor. Not a hard boss, but considering his high HP and the hype from fighting all 5 Bels (latter depending on the route), it feels awesome to fight him. Especially with the music and how his affinities change. Also, on Gin's route, you lose your demons in the second form... AND PROCEED TO BEAT IT UP ANYWAY.

Grima from Fire Emblem: Awakening

By no means my favorite game but it was a good one and introduced me to the Fire Emblem series! The thing that made Grima so good was, not only did it have a great theme, but the way I went about it. With enemies spawning from all sides and behind you, I actually rushed my avatar and Chrom all the way to the boss while everyone else rushed the sides and bought those two time. I got chills when that plan actually worked and I beat him by a hair!

Roxas in KH2. It was a short fight but what did it was the difficulty and the music. Instead of an action packed boss theme you get this song that makes you want to cry instead of fight.

Seven from Sword Art Online: Lost Song. Difficult because of maneuvering around the arena, and also landing hits. Also those text boxes that are expected to be read during battle. Fun fight though.

Nier:Automata Simone, great design, great music, and disturbing.

Oh, that's tough. Yami from Okami is pretty good. I liked how all your powers had a use. Ornstein and Snough and Artorias are fun for their difficult but fair gameplay. Other than that, I just like bosses with fun mechanics, good character and/or amazing music.

Lavos, from chronno trigger.