Dark "f*cking" Yojimbo in Final Fantasy X. You need to beat him 5 times in a row and he has Zanmato which can kill your whole team in one hit. Even Penance (the ultimate optional boss) was easier.

Paladin's Quest's final boss. The problem is that only the main character can do meaningful damage, and the attack that does so costs 250 HP (out of about 1500 if you're level is a bit above average). Leveling up that attack actually reduces the damage done by that attack. Even worse, this boss is strong enough to lower a character's HP from full to 0 in a single turn, and there's no mid battle resurrection.

I ended up using an unorthodox strategy:

Before the battle, make sure that:
1. You recruit Lilie when you reach that town. This takes a while, but she is used in the final battle. Also, get a spare LifeCor so Media can heal herself for free.
2. Media learns ATBack while in the past. (Alternatively, give her the AdultCl.)
3. You get the missable GigaBl while in the past, as well as the other one.
4. For the final battle, companions are Media and (IIRC) Hawk.

Now, for the final battle, the strategy I actually use is as follows:
1. Cast Wall. All of the final boss's attacks are physcial, no matter what they look like, and this spell makes the fight safer. At high levels, you can skip this to make the battle faster.
2. Have Chezni, Media, and Lilie cast ATBack. This causes enemies using physical attacks against the party (including the final boss) to take a portion of the damage.
3. Spend the rest of the fight having everybody use free self-heals.

The Mega Dragons are manageable with the right setup.

MM2: Use a party of Clerics so that everyone can use Mass Distortion. Spam Mass Distortion, and when the damage drops below 500, switch to using Proton Blades as items. To survive breath attacks, you can use Max HP potions and Divine Intervention.

Xeen: Have your highest level character cast Day of Protection and Power Shield via item. Then use the Xeen Slayer Sword as your weapon. You can trade it every turn, or you can use the "I LOST IT" cheat to get them for everyone. (Energy resistance would also be good here.)

Doom the Roguelike-

Defeated by Cyberdemon boss when using Scout
Defeated by Hell lord boss when using scout

Defeated Doom the Rlike game with Scout that used pistols and hellrunner

Defeated Doom the Rlike game 2nd time this time with Technician guy who uses melee weapons/ hellrunner and iron man trait

Defeated the game 3rd time with marine with similar build to scout with pistols, hellrunner and aim feat.

Beat Sarevok with Solo Kensai on highest difficulty

Defeated and couldnt beat Irenicus on anything more than normal difficulty.

Defeated by regular enemies many times on Diablo the Roguelike

Beat Diablo the Rlike and made it to hell with a rogue

Cant get past Diablo the Rlike with a warrior (was defeated)

Made it to floor 17 of Sword of the Stars the Pit with a few chars. But defeated by hunger and regular enemies

I don't think there are any bosses I have ever given up on. There are a few that have really hit me like a wall though.

Alma from Ninja Gaiden. Chapter 7 boss IIRC. She kicked my ass quite hard until I just got good enough to defeat her. Flying Swallow is the best.

Capra Demon in Dark Souls. This boss always gives me trouble. Every time. I don't think, on any playthrough, I've ever managed to beat it first go. Those *fucking dogs* kick my ass every time. If I can get to the ledge and take out the dogs before goatface killa manages to get to me I'm usually fine. Tricking him in to coming up the ledge and using plunging attacks on him is cheap but effective.

Honourable mention: Any boss with QTEs. The Kayran in Witcher 2 was a pain in the ass until I turned off QTEs. I hate QTEs.

Omega Rugal in King Of Fighters 95, for as long as I have been a neo geo fan. I've only managed to ever beat him once, on easy, by total, sheer and utter luck.

Metal Gear Solid 3: Snake Eater - The Boss.

*Spoiler*

If you didn't use any cheap tricks on her, which I wouldn't deprive the Boss of a fair fight, she was really tough hiding in the tall grass with the theme song anxiously counting down your destruction.

I was surprised I actually managed to beat her, I think by luck and shooting at everything that moved.

There's many reasons why this game absolutely awesome, The Boss is one of them.

Pretty sure tinyE counts. I mean, nobody's managed to ban him yet.

This one in Prince of Persia : The Two Thrones probably gave me the most trouble:
https://www.youtube.com/watch?v=V139qhElUpQ

Yeah, I can beaten dark Valevor, Ifrit, Shiva but dark Yojimbo is another story have to beat it 10 times if I'm not mistake and my Yojimbo is useless, paid him with lot amount of gil ended up cast daigoro or wakizaki. *sigh

Snatcher - Snatchers

I'm not a good enough Neo Kobe detective, the Snatchers killed Gillian Seed and have taken over the world. Unfortunately.

Sorry everyone, I just wasn't a quick enough draw with my laser gun. It's eminent that you will all be duplicated by Snatchers very soon.

The most difficult fight I've had was probably some arcade shmup boss, but still the most *memorable* one remains FF7 Sephiroth, for the wrong reasons.

I was playing FF7 for the first time last year, no guides, no videos, no level grinding, no nothing. I was totally unprepared and under equipped for the Sephiroth fight. Subsequently I found myself in this perpetual loop where he would do his bullshit planet buster attack, and I would barely heal/revive/buff everybody and *maybe* land a single hit for chip damage until the next turn.

This took FOUR FRIGGIN' HOURS. No kidding. And I didn't even realize because I didn't have a second to stop and look at my watch between desperately casting all sorts of healing spells.

That said, I beat it on my first try :)

The Fume Knight in Dark Souls II : SOTFS Crown of the Old Iron King area. Holy hell (literally; you have to go a whole distance down from the surface to meet him) I spent like 3 days on him trying out various weapon combos and weapon buffs and even tried a summon, with him being the only boss I ever even had so much trouble that I felt I needed a summon.

I admit I am terrible at boss battles.
Anything from the whale in The New Zealand Story to Ninja Gaiden and Dark Souls.
I know it defeats the purpose of the game, but I would gladly welcome a skip boss option.
Sad middle age old git.