I cannot stand those boss fights in JRPGs that were made to be unbeatable for storyline purposes without you even knowing it.  You come up to a boss that you are required to fight, and you pull every trick in the book to defeat him.  And after you get your ass handed to you expecting a humiliating "GAME OVER", the game continues with the boss running away to fight another day.  What the hell gives?  Yes, this is a bad thing.  Now, the good guys don't always win every battle.  But you just spent precious healing and revival items to save yourself from loosing the game only to discover that life goes on when you could have saved those items for a boss that can really end your game.  Sure, you can go back to a previous save, but what if that save were an hour or two ago?  Real time lost if you want to go back and save those items.  Even if you had saved right before that pre-planned loosing boss battle, you just spent 30 minutes of real time that you cannot get back fighting that boss.  Do they still make JRPGs like that these days?

I was reminded of this when playing Neptunia Rebirth 2, but to my relief, sort of the opposite happened.  The boss was kicking my ass.  She had those attacks that could wipe out my entire party of four in one swipe.  But when I finally won that battle, experience points were awarded, but the dialogue continued as if my characters were defeated.  So I saved the game, whet back to a previous save, and lost on purpose.  And, yes, the game continued with that same dialog.  So for once (at least for me) you can defeat a boss that wasn't meant to be beaten and be rewarded for it while the story continued as planned.

First time you fight Final Fantasy 3's final boss you can't win, but you sure as hell will waste all those precious shurikens like a fool.

You can't ever beat Beatrix in Final Fantasy IX, either. Worst part is that losing against her is a game over, so you gotta keep trying until she decides to finish the combat.

Took the words right out of my mouth, I quit the entire game when I got to that thing. Just impossible. Omega is a jack ass too. And that Emerald Weapon.

When you say "3" I'm assuming you meant "6." Right.  Never finished either one.  I vaguely remember fighting Beatrix, but I remember she's a tough cookie.

It's usually pretty easy to see what kind of fight you're in in Neptunia IMO. If the boss uses 9999 damage attacks and your first attacks are useless, just drop dead, no need to lose time or objects here ^^.

In Yu-Gi-Oh!: Forbidden Memories, there's a fight at the beginning that's almost impossible to win. However, if you do manage to win, the guy just wants a rematch and then you're put into in impossible battle. However, even counting the battles that you can win, the game is as hard as hell!

that bof4 boss.

edit: got the name, Ight

The fight in question when playing Rebirth 2 was with CFW Magic for the first time.

I see what you're saying.  She had the first move which instantly wiped out half my party.  And after reviving them, three of the four characters did little to no damage.  But only Nepgear did any significant damage.  And as long as she was constantly healed, CFW Magic was whittled away to nothing.  So after I had defeated CFW Magic, it was surprising that the dialogue continued as if the battle was hopeless.

I don't like it either. Most of times it feels like a cheap way to advance the plot.

The same goes for those cutscenes when your character acts stupid or becomes weak all of a sudden.

No, when I say 3, I say Final Fantasy III. As in the numerical third entry for Japan. xD