A further, more extensive search for the hidden Falcon and the Rebels is conducted by TIE bombers who systematically drop depth charges in the asteroid's caverns and tunnels. The Princess hears and sees a winged, leathery creature with a slimy mouth and eyes in one of the viewports, as it bangs on the ship's hull. Donning gas masks, Han and Leia go out to investigate and Han blasts the menacing Mynock with a laser bolt. But more Mynocks attack, with the potential to chew on the craft's cables and disable it. And then the wet, strange ground of the cave begins to buckle and shudder as it moves. Han orders the ship to be fired up and depart - but as they approach the mouth of the cave to exit, they see a row of sharp, jagged stalactites and stalagmites that surround the collapsing entrance -- however, it becomes clear that the cave is a creature - they are in the gullet of a giant space worm with enormous teeth! The Falcon turns sideways and narrowly escapes between two teeth, and they launch just before being caught between its jaws.

Training commences for Luke in the marshy jungles of Dagobah, where he swings on long tree vines, and his physical endurance is tested (with Yoda riding on his back). Yoda teaches his young potential Jedi knight:

Yoda: Yes, a Jedi's strength flow from the Force. But beware of the dark side. Anger, fear, aggression. The dark side of the Force are they, easily they flow, quick to join you in a fight. If once you start down the dark path, forever will it dominate your destiny. Consume you it will, as it did Obi-Wan's apprentice.
Luke: Vader. Is the dark side stronger?
Yoda: No, no. No. Quicker, easier, more seductive.
Luke: But how am I to know the good side from the bad?
Yoda: You will know when you are at calm, at peace, passive. A Jedi uses the Force for knowledge and defense. Never for attack.

Luke senses something is not right in a nearby underground cave, and Yoda urges Luke to enter its dark side and "domain of evil" - where he finds himself face-to-face with Darth Vader! The two combatants ignite their light-sabers and dueled together - and with one sweeping blow, Luke beheads Vader. But when he looks to examine the decapitated head in the armored black helmet lying on the ground, he gasps when he sees only his own face. It means he is not yet ready to face Vader.

Onboard his Star Destroyer, Darth Vader has called in the galaxy's most notorious bounty hunters to find the Millennium Falcon, offering a "substantial reward," but he orders that they must be captured alive ("No disintegrations"). However, a report from the Star Destroyer Avenger claims that Imperial fighters have already located the Falcon, and its tail (the main rear deflector shield) has been struck by a blast, crippling it from entering light-speed. With a desperate counter-attack maneuver, Han turns his ship around and aims directly for the bridge of the Avenger -- the assault tactic works as the Falcon targets the enemy, but then veers off and vanishes completely. Imperial Force Captain Needa (Michael Culver) realizes he must report to Darth Vader and apologize for their disappearance.

In the muddy bog, Luke continues to be trained, practicing balance and levitation to master the Force. He complains about his sinking X-wing fighter, now submerged in the muck, and fears he can never leave, although Luke is prompted by his mentor Yoda to not be negative, and to use the power of the Force to move objects, no matter their size. On his first try, the ship rises, but then sinks back, and Luke loses hope. Yoda demonstrates his own belief in the Force and its power and gently raises the ship from the bubbling slime, and guides it gently to dry land. Luke is dumbfounded, which is exactly Yoda's point:

Yoda: Use the force. Yes. Now, the stone...Feel it. Concentrate! (Luke collapses)
Luke: Oh, no. We'll never get it out now.
Yoda: So certain are you. (sighs) Always with you it cannot be done. Hear you nothing that I say?
Luke: Master, moving stones around is one thing. This is totally different.
Yoda: No! No different! Only different in your mind. You must unlearn what you have learned.
Luke: All right, I'll give it a try.
Yoda: No! Try not. Do. Or do not. There is no try.
Luke: (He fails in raising the ship, and it sinks lower) I can't. It's too big.
Yoda: Size matters not. Look at me. Judge me by my size, do you? Hmm? Hmph! And well you should not, for my ally is the Force. And a powerful ally it is. Life creates it, makes it grow. Its energy surrounds us and binds us. Luminous beings are we, not this crude matter. You must feel the Force around you. Here, between you, me, the tree, the rock, everywhere! Yes, even between the land and the ship.
Luke: You want the impossible.
Yoda: (after levitating the ship and setting it on dry land) Mmm...
Luke: I don't, I don't believe it.
Yoda: That is why you fail.

In front of the furious Vader, Captain Needa apologizes and falls dead. Vader commands, through Admiral Piett, that the full fleet conduct a search for the Falcon, and warns: "Don't fail me again, Admiral." Han's Falcon has not disappeared into light-speed as believed, but has clung to the side of the hull of the Star Destroyer with a landing claw, and is in hiding, with all its power circuits shut down. Han rightfully guesses that the Imperial fleet will dump its garbage before entering light-speed, and they will be detached among other debris. He then sets course to navigate to a "safe port" -- a small tibanna gas mining operation at Bespin owned by his old friend Lando Calrissian (Billy Dee Williams) - "a card player, gambler, scoundrel." However, there is one ship silently trailing the Falcon - the ship of bounty hunter Boba Fett (Jeremy Bulloch).

More difficult lessons are provided by Yoda to give Luke an understanding of the Force, stressing: "You must learn control." Luke suddenly feels a powerful wave of fear and has a terrible future vision of his friends (Han and Leia) in pain and danger - "I saw a city in the clouds." Yoda cautions him about leaving prematurely: "But you would destroy all for which they have fought and suffered." The floating Cloud City that Luke envisions was on the planet Bespin, where Han has flown the Falcon for refuge and repairs on the hyperdrive. Cape-wearing Lando greets them after they are permitted to land - warmly hugging Han after first hiding his friendship with him: "How you doing, you old pirate?!" According to Han, Lando lost the Falcon to him "fair and square." Lando also meets the Princess, and uses his smooth charm on her. As he leads them inside the citadel, C-3PO lags behind and walks through a doorway into a restricted area when he hears a familiar R2 unit -- after intruding into a locked chamber, he is blown apart by a blaster.

Luke continues to be impatient and wants to prematurely leave Dagobah to aid his friends. He ignores Ben's advice about leaving before he is a fully-trained Jedi knight, and about facing temptation from the dark side and becoming an agent of evil:

Yoda: You must not go.
Luke: But Han and Leia will die if I don't.
Ben's voice: You don't know that. Even Yoda cannot see their fate.
Luke: But I can help them. I feel the Force.
Ben's voice: But you cannot control it. This is a dangerous time for you when you will be tempted by the dark side of the Force.
Yoda: Yes! Yes! To Obi-Wan you listen. The cave. Remember your failure at the cave.
Luke: But I've learned so much since then. Master Yoda, I promise to return and to finish what I've begun. You have my word.
Ben's voice: It is you and your abilities the Emperor wants. That is why your friends are made to suffer.
Luke: That's why I have to go.
Ben's voice: Luke, I don't want to lose you to the Emperor the way I lost Vader.
Luke: You won't.
Yoda: Stopped they must be. On this all depends. Only a fully trained Jedi knight with the Force as his ally will conquer Vader and his Emperor. If you end your training now, if you choose the quick and easy path as Vader did, you will become an agent of evil.
Ben's voice: Patience.
Luke: And sacrifice Han and Leia?
Yoda: If you honor what they fight for, yes.
Ben's voice: If you choose to face Vader, you will do it alone. I cannot interfere.
Luke: I understand.
Ben's voice: ...Luke! Don't give in to hate. That leads to the dark side.
Yoda: Strong is Vader. Mind what you have learned. Save you it can.
Luke: I will, and I'll return. I promise.
Yoda: Told you, I did. Reckless is he. Now, matters are worse.
Ben's voice: That boy is our last hope.
Yoda: No, there is another.

In the Cloud City on Bespin, Chewbacca finds the disassembled parts of golden droid C-3PO on a conveyor belt in a junk room, and brings the pieces to the living quarters provided for Han and Leia. As Lando invites them away for refreshments, he describes how he has recently made a deal that will keep the Empire out of his small mining business operation. As he opens a door to a room with a long banquet table, the figure of Darth Vader emerges at the head of the table. Han draws his blaster and fires, but the shots are deflected and the weapon is seized from his hand. Lando apologizes and admits that he has no choice, since the stormtroopers and bounty hunter Boba Fett arrived right before they did to force the deal. Chewie is confined in a prison cell with C-3PO's disattached parts - and tries to reassemble and reactivate the droid, by placing its head on its torso, although at first, he has the head on backwards. Nearby, Han is also imprisoned - held by straps and lowered onto a torture device that sends electric shocks through his body. The menacing, double-crossing Vader instructs Boba Fett: "You may take Captain Solo to Jabba the Hutt after I have Skywalker," and tells Lando that Leia and the Wookiee must never leave the Cloud City, reversing previous agreements he has made with Lando. A battered and bruised Han Solo and Leia are flung into Chewie's cell, where Lando tells them that Vader is turning Han over to a bounty hunter, and that Vader is setting a trap for Skywalker, using them as bait: "He's after somebody called Skywalker." Han fights back and slugs Lando, but is subdued by Calrissian guards.

A primitive and crude chamber, a platform within a pit surrounded by pipes, hoses, and tubes of chemicals, is prepared by Vader. It is a carbon-freezing facility to be used to immobilize Skywalker, already on his way in his X-wing fighter to the planet, so that he can be frozen and transported undamaged to the Emperor. Vader's intention is to first test the freezing chamber on Han Solo, and Chewie vainly fights off some of the stormtroopers until Solo calms him and tells him to "save his strength - there will be another time." Princess Leia kisses Han as he is about to be dipped in a carbonite-freezing chamber - she confesses: "I love you" to which he replies: "I know." Moments later after Han is encased in carbonite, big mechanical tongs extract the thick metal block from the pit and it is laid flat on the platform - showing his imprint. Calrissian declares that Solo is still alive and has survived the freezing process ("and in perfect hibernation"). Vader turns Han over to bounty hunter Fett. Vader orders preparations of the chamber for their new arrival, and then alters his deal with Lando - specifying that the Wookiee and Leia will be taken to his ship.

On guard, Luke flies into the Cloud City without any patrol ships or signs of hostility, and enters a passageway-corridor with R2-D2 as they progress to the central plaza, watching as Han's encased body is pushed along and followed by armed stormtroopers. Luke also sees the Princess, Lando, a disassembled C-3PO and the Wookiee being led by other stormtroopers down a second corridor and hears Leia calling out a warning to him: "It's a trap." He finds himself in the large carbon-freezing chamber where he senses Vader's dark presence, and then sees his silhouetted figure: "The Force is with you, young Skywalker. But you are not a Jedi yet." They ignite their light-sabers and begin to duel. Meanwhile, as Lando and the others are led by a squad of stormtroopers, he alerts his men to ambush the Imperial guards at an intersection - he then disarms them, imprisons them in a security tower and acquires their weapons. He tells Leia: "We're getting out of here" while releasing Chewie's bindings. Lando pleads for them to trust him: "I had no choice...There's still a chance to save Han at the east platform." But they are too late - Boba Fett's ship has already taken off.

The duel continues - Vader sends Luke's light-saber flying from his hand, and propels the young Luke down a flight of stairs. Vader threatens: "Your destiny lies with me, Skywalker." Luke is forced backward into the open pit and into the freezing chamber, where freezing steam rises. But Luke leaps in a streak out of the pit before it is activated and holds onto some hoses above Vader's head. Luke's light-saber jumps into his outstretched hand and they continue to fight, with Vader admitting how he is impressed. He taunts: "Release your anger. Only your hatred can destroy me." With one swing, Luke sends Vader falling backward, but then he reappears in a lower level of the freezing chamber, in the control room. Vader sends huge pieces of pipes and machinery hurtling toward him, although Luke uses the Force to dodge and deflect them. But various chunks of metal eventually knock him down and suck him through a window and into the reactor room - where he is hanging above a bottomless space below. [During their escape, Lando announces to his Cloud City citizenry to evacuate before more Imperial troops arrive. Under heavy fire, they make their way to the Millennium Falcon, and activate its engines to escape.]

Luke finds himself standing on a narrow gantry high above a wind tunnel, where Vader meets him again. Although Vader predicts Luke's defeat ("You are beaten. It is useless to resist. Don't let yourself be destroyed as Obi-Wan did"), Luke strikes back with a vicious lunge and hits Vader in the upper arm. Vader retaliates and as Luke glances away at a destroyed instrument panel, his right hand is struck at the wrist with Darth Vader's saber, and is amputated. As Luke retreats, Vader entreats with an outstretched arm, and ultimately delivers a startling revelation:

Vader: There is no escape. Don't make me destroy you. Luke, you do not yet realize your importance. You have only begun to discover your power. Join me, and I will complete your training. With our combined strength, we can end this destructive conflict and bring order to the galaxy.
Luke: I'll never join you!
Vader: If you only knew the power of the dark side. Obi-Wan never told you what happened to your father.
Luke (glaring back): He told me enough. He told me you killed him.
Vader: No, I am your father.
Luke (horrified and gasping): No, no. That's not true. That's impossible!
Vader: Search your feelings. You know it to be true.
Luke: No! No!
Vader (promising): Luke. You can destroy the Emperor. He has foreseen this. It is your destiny. Join me and together, we can rule the galaxy as father and son. Come with me. It is the only way.

With no other alternative, Luke steps off the platform and falls into the chasm.

After tumbling through various shafts and pipes, he hangs onto Cloud City's weather vane beneath the large floating structure, and desperately calls out for Ben to help him, but there is no response to his plea. He then appeals to Leia, calling out her name. Somehow, she hears his cries and demands that they go back to Cloud City, amidst TIE fighters and a complete evacuation. They find the battered Luke hanging underneath the City, maneuver the ship perfectly underneath him, and open the top hatch as he drops into the Falcon. They then retreat from TIE fighters and prepare to jump into light-speed with the supposedly-repaired hyperdrive. [Now back on his Star Destroyer, Vader announces that he ordered the deactivation of the hyperdrive and is preparing a tractor beam to capture them and board the freighter.] Vader calls out for Luke, who responds: "Father." Vader requests: "Son, come with me," as Luke also cries out for Ben, asking: "Why didn't you tell me?" Vader adds: "Luke, it is your destiny." Before their capture by the tractor beam, R2-D2 repairs the hyperdrive and the Falcon's occupants are thrown backwards by its thrust. Vader watches helplessly as his prey disappears.

Rebel forces assemble in another distant part of the galaxy, where on a medical frigate, Luke's hand is being treated and replaced with a bionic one. On the Falcon with Chewie as he departs, Lando communicates that he will begin a search for Jabba the Hutt and his bounty hunter - to find Han Solo. Lando plans to meet up with Luke at a rendezvous point on Tatooine. Luke's final words to Lando are: "May the Force be with you." Princess Leia, Luke, and the two droids watch through a wide viewport as the Falcon races from the Rebel cruiser through the sky after takeoff.