The main story is meant for everyone to be able to complete, and experience the story for themselves. For a game like Final Fantasy to cut out a part of their playerbase because they aren't "good enough" would be stupid.
Superbosses on the other hand, go ahead.
A superboss is an optional boss that is very powerful, normally even more so than the game's final boss, and generally gives either large amounts of experience, rare items, or both. In the Final Fantasy series, they are usually found deep at the end of optional dungeons, or can only be found after a long series of sidequests. They normally have no bearing on the storyline, and their existence is rarely explained.
Likewise, the rewards gained from defeating a superboss are often not particularly useful—sometimes they give a key item as a proof of defeating the boss—as the player must already be extraordinarily skilled to defeat the boss in the first place, they thus have no need for further battle enhancements afterwards. Superbosses exist to challenge the player and give them something to do once the main storyline is finished.
Final Fantasy - Warmech (random encoutner) (nerfed in later versions), Shinryu and Omega (Dawn of Souls+), Chronodia (20th Anniversary+)
Final Fantasy II - Iron Giant (random encoutner), Astaroth and Beelzebub, Ultima Weapon (Dawn of Souls), Phrekyos (20th Anniversay+), Deumion (20th Anniversary+)
Final Fantasy III - Iron Giant (3D remakes)
Final Fantasy IV - Zeromus EG (GBA+), Brachiorados (GBA+), Geryon and Proto-Babil (3D remakes)
Final Fantasy IV: The After Years - Omega, Lord Dragon (Shinryu), Ultima Weapon, Lost Babil (PSP Post Game), Lunar Dragon, Lunar Odin, Lunar Leviathan, Lunar Bahamut (Mobile)
Final Fantasy V - Omega, Shinryu, Omega Mk.II and Neo Shinryu, Enuo (GBA)
Final Fantasy VI - Kaiser Dragon (originally planned to be the superboss for the SNES, but dummied for unknown reasons), Deathgaze, Kaiser Dragon (GBA, finished version), Omega Weapon
Final Fantasy VII - Emerald Weapon, Ruby Weapon (both didn't exist in the japanese version, so Ultima Weapon was theirs)
Crisis Core -Final Fantasy VII- Minerva
Final Fantasy VIII - Omega Weapon
Final Fantasy IX - Ozma, Hades
Final Fantasy X - Ultima Weapon and Omega Weapon, Nemesis, Dark Aeons and Penance (PAL and HD Remaster)
Final Fantasy X-2 - Angra Mainyu, Major Numerus and Almighty Shinra (HD Remaster)
Final Fantasy XI - Absolute Virtue, Pandemonium Warden, Kirin, Dynamis Lord, Paramount Botulus, Paramount Gallu, Ark Angels, Carbuncle Prime, Bahamut, Odin, etc
Final Fantasy XII - Yiazmat, Omega Mark XII, Zodiark, Five Archadian Judge Magisters (HD Remaster)
Final Fantasy XII: Revenant Wings - Yiazmat, Final Boss and his minions (if you compelte all missions, both him and his minions will be max level)
Final Fantasy XIII - Vercingetorix, Long Gui
Final Fantasy XIII-2 - Long Gui, Yom, Raspatil, Snow, Gilgamesh, Valfodr (DLC)
Lightning Returns: Final Fantasy XIII - Aeronite, Ereshkigal, Bhunivelze (NG+)
Final Fantasy XIV - Ifrit (extreme) and Nael Deus Darnus (both Legacy), Ultima Weapon, Odin, Bahmut, Nael Deus Darnus, Alexander, etc
Final Fantasy XV - Around 10 Superbosses (I personally didn't look up the names)
Final Fantasy Tactics - Elidibus, Ultima
Final Fantasy Tactics Advance - Corrupt Judges, Li-Grim
Final Fantasy Tactics A2: Grimoire of the Rift - Magick Weapon, Clan Ciquleur Members
Final Fantasy Type-0 - Nox Suzaku, Gilgamesh
Vagrant Story - Asura
Final Fantasy Crystal Chronicles: My Life as a King - Omega, Wyrm
Final Fantasy Crystal Chronicles: Echoes of Time - Great Galdes
Dissidia Final Fantasy - Chaos
Dissidia 012 Final Fantasy - Haniwa (random encoutner)
Final Fantasy Legend II
Final Fantasy: The 4 Heroes of Light - Krinjh, Torte, Rolan and Rekoteh, The Adventurer and Faithful Fox
Bravely Default - The Adventurer
Final Fantasy Dimensions - Adamantoise, Ω Weapon, Gigantuar