Well there are two that spring to mind. I'd actually be surprised if anyone else here has fought them since most people here seem to have mainly played Final Fantasy, some Tales games and a few other JRPGs, but I don't think I've seen these games mentioned. Even if you have played either of them, you have to put in a lot of work to get to them. I personally fought Freya (and died horribly) but didn't get to Demi-Fiend. I can understand how hard he is, though, since I've played DDS1 and DDS2 a lot. To fight Freya you have to do an insane amount of stuff after the "final" boss and to fight Demi-Fiend you have to complete DDS twice.
Freya, Star Ocean 3.
Originally, I just wrote several paragraphs trying to convey how hard it is, but it'd be pointless if you hadn't seen her with your own eyes and pointless if you
had. It's just that first of all, SO3 is played in real-time with a fairly complex battle system similar to a 3D fighting game. This means that even if you know exactly what to do, you can't just mechanically proceed to do it in a turn-based style; you still need to skill and dexterity to be able to pull it off. Add to that fact the other fact that you need to customise your own armour and weapons and you see that it's not like in most RPGs where you just get
the best set of equipment, level to max level and then easily kill the boss. Damn, and now I've made myself want to play SO3 again...
Demi-Fiend, Digital Devil Saga
Now, to go against what I've just said, a genuinely hard turn-based boss is the Demi-Fiend from DDS1. It's super hidden boss that you have to play through twice to see. He's actually the main character from SMT Nocturne. Even if you are max level, have optimal equipment and set-up, do exactly what you're supposed to... He can still kill you easily. To be honest, I think it's bad that luck comes into so much (unlike in Star Ocean or the Tales series, or in TWEWY, where if you've got the skill, you can theoretically do almost everything at level 1) but still, it does make him probably the hardest turn-based RPG boss that comes to mind.
The comments of the uploader on YouTube:
This boss is the main protagonist from Shin Megami Tensei III: Nocturne, known as Demi-fiend or Hitoshura. In DDS, he's the hardest optional boss you face in a Clear Data.
One of the hardest bosses in RPG history, you don't stand a snowflake's chance in hell unless you have the ultimate level 99 party with the best skills, along with stat-boosting items. Not only does this fight require a complex strategy, but you need the luck of the Irish to survive this onslaught.
Part 1: Intro (0:00-1:47)
Part 2: Surviving Gaea Rage* (1:47-3:27)
Part 3: "Stun Locking" Pixie and Arahabaki (3:27-4:37)
Part 4: Finishing Demi-fiend off (4:37-5:42)
*I'm supposed to get hit by Dormina and use Null Sleep to avoid Gaea Rage, but luckily I was able to get a Close Call instead.
I used the infamous "Red Star" strategy.