Welcome to the full lowdown on FFU's story, episode by episode! Enjoy!

Episode 01: "Wonderland, Journey into the Darkness"
A giant dark pillar appears in the ocean off of Tokyo. Two huge beasts appear out of it, a red one with the head of a gun, and a white one with the head of a sword. They attack each other and both are destroyed. Joe and Marie Hayakawa, a geologist couple, are swallowed into the pillar and end up in a crazy place called the Inner World. They return safely after many adventures.
Twelve years later, the pillar is a tourist attraction. Joe and Marie have gone into the Inner World again to explore (after writing a bestselling book on the flora and fauna of the place), and are never seen again. Their twin children, Yu and Ai, enter an abandoned subway station to ride the Inner World subway to look for their parents. However, the train has another occupant - a woman named Lisa Pacifist, also traveling to the Inner World for reasons she refuses to divulge.
Arriving in the Inner World, they encounter a strange land that looks like Tokyo, but is inhabited by insects and built out of plants! Yu encounters a chocobo, who pulls Ai's pigtails and runs off. He then trips over someone's leg. The leg belongs to a man called Kaze, who has been put to sleep and trapped in a plant cage. He awakens at Yu's touch.
Suddenly, what looks like a flying saucer drops a crystal that turns into a mushroom monster! Lisa staves it off with a power called kigenjutsu, but it just gets angrier and bigger. Lisa and the kids end up hanging off the edge of a cliff with the monster before them. However, Kaze is nearby and uses his Demon Gun to summon Phoenix and destroy the monster from inside. However, he has an unnoticed observer by the name of Oscar...
Episode 02: "Magun, Man of the Black Wind"
Kaze walks off, ignoring the parting words of Lisa and the children. In the meantime, Fungus (the person inside the flying saucer) returns to Gaudium, the home of Earl Tyrant, and we are introduced to three of Earl Tyrants's Deathlords, Fungus, Herba, and Oscar. Oscar creates a puppet named Crux, who tails Kaze. Fungus is given the task of getting rid of Lisa and the others. In the meantime, said targets meet the chocobo again; he has a contraption around his neck now. They follow him into a forest, where they meet a crazy old lady named Chocobaba.
Chocobaba's fairly useless, but after she runs off Yu finds a chocobo feather. However, they're attacked by another mushroom monster and cornered. Yu's chocobo feather glows and appears to call his chocobo, who attacks one of the monsters. It's still not enough, and things are looking dim, until Kaze arrives and blasts them to oblivion. He wants to ask Yu something, but before he can Fungus arrives. Kaze's Demon Gun is put to good use (this time with Typhoon) and Fungus disappears. Kaze asks them if they've seen a man named Shroi Kumo (having remembered his name), but they haven't, of course. Yu tries wearning his chocobo feather and finds that he can read the chocobo's mind, which tells him to hurry and catch the subway before it leaves!
Episode 03: "Fruit, The Town of Sweet Scent"
In Gaudium, Fungus is resurrected at a fraction of his original size. 8-) Oscar believes Kaze might be the Unlimited, one whose power rivals the gods'. In any case, Herba wants to see the Demon Gun for herself. Lisa and the kids get off the subway in a place where everything is made of fruit. Kaze's already there before them, though. O_o Everyone here wears hooded cloaks and talks depressingly. Ai's bag is suddenly stolen by one of them, and she chases after him, getting cut off from Lisa and Yu. She finds Kaze asking about Shroi Kumo again, but being redirected to Gaudium for his inquiries. She loses the thief. However, the sound of the ocean leads her to the home of Fabra, the Guiding One, inside a giant oyster shell.
Fabra gives Ai a little monster named Pochepoke to help her, then disappears. Herba enters now, on her own flying contraption. She makes a whole bunch of flower monsters, then showers everyone with pollen that does the same thing as laughing gas. Kaze aims the Demon Gun, but it doesn't want to work. Instead, he shoots down the flower monsters, but only succeeds in increasing the pollen. Ai asks Pochepoke for help, and gets it in the shape of an explosive watermelon seed which disperses the pollen. The Demon Gun decides to work now, and Kaze summons Shiva. A frozen Herba runs away. Ai reunites with Lisa and Yu, but Izabel, the clock on the chocobo, rings out, indicating that the subway's leaving! They rush to catch it...
Episode 04: "Makenshi, The White Etude"
...but they miss it! However, a face pops up from one of the nearby tiles - it's the one who stole Ai's bag! (Unfortunately, he ate it already. 8p) He introduces himself as Fungo, and takes them underground to the base of the Comodin, an organization trying to bring order to the Inner World. They meet its leader, Knave, his second-in-command, Mireth (who gives Ai some new clothes), and its braniac inventor, Sid. Kaze's there, too.
Sid heals the chocobo from residual weirdness from flower pollen with Genevieve, his "all in one healer". However, the fun is cut short when Shroi Kumo pierces the base's cover. One big explosion later, Ai and Yu are unconscious, the Comodin are out of commission, Lisa has a flashback of the white beast in Tokyo 12 years ago, and Kaze is duking it out with Shroi Kumo, uncaring about the havoc he's causing. However, his Demon Gun refuses to fire, and Shroi Kumo destroys everything around him...
Episode 05: "Sid. The Adventure of the Underground Waterway"
Sid prepares his river vessel, Catharine, to take Lisa, Ai, and Yu back to the subway. Mireth provides them with some instant food, but Pochepoke eats half of it in one gulp, prompting Ai to muffle it. 8p They take off, but are interrupted by Fungus, back to full size, riding a giant serpent named Viking. He gives chase...
They manage to get rid of him with the help of several secret James Bond-style gadgets and the chocobo's super kick... but not for long; a surprise attack damages Catherine. Sid goes nuts, breaks out a bunch of crazy machines, and hammers Fungus flat. 8p Lisa, Ai, and Yu run for the subway, leaving a heartbroken Sid behind. However, Fungus shows up again, only to be killed again by Kaze's Ixion summon. Sid is forced to leave Catherine behind in the explosion. The wanderers manage to catch the subway and escape.
Episode 06: "Kigen Arts, The Savior of Souls"
Yu picks a name for his chocobo: Chobi. They land in a desert punctuated with pillars of fire. Unfortunately, one closes the subway entrance! They start walking, and Chobi leads them to an oasis. However, they're attacked by Herba and a bunch of plant spiders. Lisa uses her kigenjutsu to blow some away, letting Ai, Yu, and Chobi escape, but is herself trapped by Herba...
Ai tries to get Pochepoke to help, but only gets junk. Lisa has a flashback of her training with her mother and manages to destroy the tree she's tied to and escape. She then tries to use her kigenjutsu on the water, but fails to read it properly (the Elenium inside it reacts crazily) and sets it on fire! Herba runs away, but the four wanderers are thrust into a deep geyser, and Ai ends up unconscious. The plant spiders surround them again. Lisa tries to use CPR, but it isn't working. Kaze shows up, but the Demon Gun isn't firing, and he's eaten! Lisa manages to use nature's energy to save Ai, and Kaze summons Bismarck from inside the plant spider and wipes them all out, taking the oasis with them. However, an earthquake then erupts, leaving the four wanderers falling to an uncertain fate...
Episode 07: "Subway. Enemy of the Dimensional Tunnel"
They land on sand which cushions their fall, and right near the subway, too! Kaze goes with them this time, though (dazed by a flashback caused by Yu taking his hand). They meet another person on the subway this time: Lou Lupus. They explore the subway, but it's then attacked by Omega, an extremely destructive creature...
Lou explains that Omega destroys everything, and that it was broken up but its parts seek to become whole again. She also says that her own world was destroyed by it. She then asks for a mirror (provided by Pochepoke), looks into it, and transforms into a wolf-like form. She jumps on top of the subway and uses an energy attack against Omega, but it fails and she is sucked into it. Kaze's Demon Gun decides that now's a good time, and he summons Ifrit, which dissipates Omega. Lou comes riding back to the subway on the tail car (swallowed by Omega earlier).
Episode 08: "Soil, The Heart of the Magun"
The wanderers end up in another desert, this one with pillars of sand (or rather, Soil!) instead of fire. Lou, having fallen for Kaze, tries to look for him. In the meantime, Pist, the fourth Deathlord, returns to Gaudium after completing his Ocean Puzzle. He demonstrates his plans for beating Kaze on Shroi Kumo, stopping him from using his mist attack by blasting the vial out of his hand with a water gun (although Shroi Kumo makes sure he knows that can only work once!). Lou finds Kaze in a sand drift, but their reunion is interrupted by Pist. Kaze begins dissolving his Demon Gun (despite the huge wind it brings), but Pist quickly uses a monster called Sand Sword to steal the Demon Gun and put it on his own hand!
Lou uses a dentist's mirror provided by Pochepoke to transform and distract Pist while everybody escapes down a hole in the sand. However, he quickly finds them with Crux's help. Too fast for everyone, he soon has them all trapped in pieces of the Sand Sword. Lou mentions Omega, which surprises him. However, Kaze goads him into using the Demon Gun. He tries to summon Bahamut(?), but the Demon Gun backfires and ends up back on Kaze's hand (only he can fire it). Pist returns to Gaudium and all the Deathlords begin the search for Omega...
Episode 09: "Oscha - The Endless Project"
The wanderers end up in a place with two huge assembly lines; workers on one end partly assemble an object, while on the other end it's disassembled. Lou tells the party that they do this to survive the chaos of the Inner World. Back in Gaudium, all four Deathlords are sent to find pieces of Omega. Oscar decides to go off on a tangent after hearing from Crux, though... the workers find themselves finally completing the object they're making... when it's done, they all collapse from existential uncertainty. The object then turns into a giant robot which chases them...
Oscar appears and has a bit of witty repartee with Kaze. Kaze uses his Demon Gun while Lou defends him from the robot's attacks. Odin destroys the robot. A tiny robot emerges from the wreckage, but is kicked to death by Chobi. 8-) Kaze disappears again, and Lou (still insanely in love with him) goes off to search for him.
Episode 10: "Mansion. The Memory of Sagiso"
The subway drops them off in what looks like a town, but all the houses are pure stone. Yu spies what looks like his parents (the backpacks are theirs) walking far off! They chase after them into a huge mansion, but can't find them. They end up in a room with a bunch of Dead Peppers (huge spicy peppers) hanging from the ceiling. Chobi loves 'em, so he grabs one, but goes nuts and runs around like crazy, hooking Ai by the pigtails while he does so and separating himself and her from the others. Yu runs after them, but gets lost. Lisa, however, hears the crying of a small boy, who calls himself Sagi, and they wander the mansion together, trying to find the exit...
A contraption made by Oscar puts everybody back together - with Herba and her pet flower, Hughug! She's apparently looking for Omega, without success. She also shows them Yu's "parents": cactus creatures wearing the backpacks, which she refuses to say where she got. The contraption opens yet again, but this time Kaze steps out! He wreaks havoc with Atomos (Herba runs away first, natch). The others are almost sucked in with the mansion, but Sagi's idea to feed Chobi another Dead Pepper (from Pochepoke) works, and they run away at Spicy Speed. 8p When they come to, Sagi is gone, but in the ground is a sagisou (egret orchid). Lisa suddenly remembers a sagisou she talked to as a child, but left behind when she moves to another country, and realizes that Sagi was that flower...
Episode 11: "Ciel. The Departure of Chocobo"
The party reaches a field, where they encounter a herd of chocobos being chased by a mushroom monster. With the help of Lisa and Chobi, the herd destroys the monster. They meet Chocoimo, Chocobaba's younger sister, but she can't help them (naturally). Isabel rings and the humans start to leave, but Chobi stays behind with the herd.
The subway is again attacked by a part of Omega. Yu is separated from the others by a large gorge. In the meantime, the Chocobo herd comes across the ruins from the time of Ciel. Chobi touches them and is transformed into the Ciel chocobo. He flies to Yu and saves him from Omega. Kaze summons Titan to attack Omega, and the others escape on the subway.
Episode 12: "Fungus - Eternal Life"
The members of Gaudium begin collecting crystals of Omega (in their inert forms). Shrio Kumo collects a particularly large specimen, and in gratitude Earl Tyrant makes him the fifth Deathlord. Fungus, on the other hand, collects zip. Earl Tyrant gets angry and with Oscar's help begins a plan to get rid of Fungus to feed Chaos. Oscar shows Fungus the part of his world that was absorbed into the Inner World. By another incredible coincidence, the party (including Kaze) end up in the same place and are confronted by Fungus.
Fungus grows enormous due to the energy on his homeworld. Kaze attempts to beat him by first summoning Ixion, then Phoenix, but Fungus continues to regenerate each time. Lisa, Yu, and Ai circle around on Chobi/Ciel to see the outcome...
Episode 13: "Meteor. Abominable Memory"
Lisa jumps off Chobi and tries to reach Kaze. Her kigenjutsu causes spores to fill the air. Fungus attacks with random rocket-mushrooms, and ends up capturing Chobi with Ai and Yu. Lisa tries to stop Kaze from attacking Fungus for fear of hitting the children, but Kaze refuses to listen. Fungus captures them both with another mushroom and throws them underground. Inside a spore-filled cave, Lisa tries talking to Kaze again, unsuccessfully. Shroi Kumo suddenly shows up and attacks Kaze, making a reference to the fact that Kaze can't fire the Demon Gun whenever he wants.
In the meantime, Fungus (back to normal size) has captured the children and Chobi. He explains to them that the Inner World will absorb all the Outer Worlds and chortles about their impending execution, but is interrupted by Shroi Kumo, who tells him Kaze is still alive and invites him to finish the job. Fungus grows again, with the capturees tied to his giant mace. Lisa and Kaze run out from underground to see Fungus threaten to crush the children. However, Crux picks this time to sow a destructive mold around the place (the same mold that destroyed the world the first time). Fungus begins to crumble with the rest of his world. The Demon Gun picks this time to allow Kaze to fire it, summoning Meteor Master to totally destroy Fungus and his world along with him. Chaos feeds off Fungus's destruction; Earl Tyrant is quite pleased.

FFU Episode Guide Part 2