Part I: Mustafar

“It's over Anakin! I have the high ground!”
Obi-wan Kenobi stood safely on the bank of the lava river on Mustafar, away from the searing heat of the lava river. On a floating mining platform near the edge of the molten river, his wavy hair waving in the rippling heat, his brow beaded with sweat, former Jedi Knight Anakin Skywalker, now Sith Apprentice Darth Vader, surveyed the terrain above him, his lightsaber held low to the side. The blue blade starkly contrasted with Mustafar's fiery red glow, as did Kenobi's. Vader regarded Obi-Wan with defiance .
Kenobi knew what Vader was planning to do. “Don't try it!”
Vader said nothing but seemed collected and determined as he jumped off of the floating mining platform and landed on ths shore, close to the edge, safely away from Kenobi's glowing blue blade. Kenobi warily held his blade in front of him. Intense heat rippled around Vader's legs from the lava behind him, but Vader was easily able to keep the damaging heat at bay by shielding himself with the force as both he and Obi-Wan had done as their duel took them from the relative safety of the Separatist bunker's landing platform all the way out to the dangerous lava flow itself. Moments before both of them had been dueling on the small mining platform that Vader had just vacated. The platform meanwhile had drifted away from the embankment and had continued its preprogrammed course.
Obi-wan held his blue blade in his typical Soresu defensive position as Vader cautiously walked toward him. Anakin was in his fighting prime and much stronger in the force than he was, not to mention younger, and the duel had taken it's toll on Kenobi. As Vader moved closer, he struck with his blade and Kenobi met it with his own. Vader hammered Kenobi's defenses with brute force as he was accustomed to, but Kenobi's Soresu lightsaber style was extremely defensive, designed to block all attacks. Suddenly, the blades locked, two humming shafts of blue energy straining against each other. Sparks flew as both men pushed harder, trying to break the saber lock, their feet sliding on the loose volcanic gravel.
Kenobi looked at Vader's face. He barely recognized the face he had seen so often for the past few years. The man whom he had trained from youth and had fought beside him for the past three years of the Clone Wars was gone. Palpatine had seen to that. Ever since the Battle of Naboo, thirteen years ago, he had kept his eye on Anakin, seemingly mentoring him to be a better Jedi, but at the same time cultivating Anakin's arrogance and setting the stages for his eventual fall to the Dark side. Kenobi allowed Anakin's friendship with the chancellor to continue, not realizing what was going on until it was too late. Palpatine had shown Anakin much about the dark side while Kenobi had been on Utapau, and already, that basic training in the dark side was working against Kenobi. As Anakin gritted his teeth in anger from across the lightsaber blades, Kenobi was stunned to see that Anakin's blue eyes had changed to deep fiery yellow as his former apprentice called on the Dark side and allowed it to fill him. Vader's strength suddenly increased significantly, and Kenobi knew that he could not maintain the lock much longer.
Determined, Kenobi moved his blade back away from Vader's, breaking the lock. However, Vader executed a perfect flowing water cut, moving his blade closer towards the spot that Kenobi had just vacated. In an attempt to get away from Vader's blade, Kenobi used Ataru acrobatics to jump behind Vader in order to attack his unprotected flank. Even though Kenobi held his blade to protect himself from a retaliatory blow by Vader, his jump momentarily left him with insufficient leverage to protect against the raw power of Vader's Djem So style.
Vader capitalized on the opportunity, and with a powerful spin and cutting upwards stroke executed with speed and power that only the dark side of the force could allow, he powered through Kenobi's defense and knocked Kenobi's lightsaber aside for only a second. Kenobi attempted to counter, but his error left enough time for Vader to continue with his upward cut and slice Kenobi's left foot off at the ankle. The severed limb landed further down the slope and slid closer to the lava, starting to burn as it did so.
Kenobi landed hard on his back, his lightsaber flying out of his grip. It spun through the air and landed at the edge of the bank, the loose rocks stopping its momentum and preventing it from rolling down the slope. Despite his injury, Kenobi managed to sit up and attempted to use the force to retrieve his lightsaber, but Vader was much stronger with the force and was able to wrestle Kenobi's mental grip from the weapon. With a pushing gesture of his artificial right hand, Vader gave Kenobi's lightsaber a shove with the force and sent it rolling down the slope and into the lava. As the saber rapidly heated as it sat partially submerged in the lava flow, the power cell exploded, cracking the casing of the lightsaber handle. The lava quickly began to melt the shattered pieces. The blue focusing crystal that was the heart of Kenobi's blade cracked as soon as the lava touched it and disintegrated in a puff of smoke barely distinguishable above the volcanic fumes. The lightsaber's noncombustible metal pieces were quickly reduced to a puddle of liquid durasteel floating on top of the denser lava flow. It lingered only for a moment until the current of the river carried it over the searing lava waterfall to mix with the sea of lava far below.
Kenobi attempted to get to his feet, but Vader easily kicked him to the ground with his boot and deactivated his lightsaber but kept it ready. Kenobi tried to roll over onto his knees, but Vader kicked him again, this time in the head.
The volcanic gravel was hot even this far above the lava river, and Kenobi could smell his hair starting to singe where it touched the hot gravel. He controlled the pain from his amputated foot and other injuries with a simple Jedi technique. As with all lightsaber wounds, the wound was cauterized even as it was being inflicted, so there was no bleeding, but Kenobi could still feel the remnants of the pain that Vader's blade made as it cut through his flesh and bone.
Vader saw his former master humbled on the ground before him, much as Count Dooku had been not long before on the Invisible Hand. Vader smiled, but not for Kenobi's benefit. “The Jedi have been humiliated for their treachery against the Republic...You have been the salvation of the galaxy and will be forever honored for your accomplishment” Sidious had told him after he reported the success of the 501st legion in assuming control of the Jedi Temple. Sidious had then instructed Vader to go to Mustafar, where everything initially went as expected but he had been surprised by Padme and Kenobi. He still had a job to do, and it was time to finish it; Sidious had told him to kill all resistance on Mustafar as an additional executive order. For Padme, Vader was definitely willing to make an exception to the order, but Kenobi still had to be dealt with.
Vader stretched out his artificial right hand and lifted Kenobi off of his feet with the force and brought him into striking range. In his left hand, Vader still held his deactivated lightsaber. Kenobi raised his head and looked at Vader. The hot volcanic rock had singed half of Kenobi's beard away and created a blistered burn on his face. Struggling to speak against Vader's crushing grip, Kenobi had only one thing to say.
“Anakin.....Why?”
Vader made his reply simple. “For Padme.”
Without wasting further words, Vader ignited his lightsaber and speared the tip of the blade through Kenobi's chest.
Kenobi remembered his master Qui-Gon Jinn, who had been killed in a similar way, also by a Sith. As Vader's blue blade stabbed toward him, entered his chest, and immediately pierced his heart, Kenobi strangely felt a sense of calm as he released his hold on his dying body and became one with the force. The once venerable Jedi master went limp and gasped through Vader's force-powered grip as his last breath left him.
Vader released his force grip and allowed Kenobi's lifeless body to slump to the ground in front of him. Just as with Dooku, he had killed in service to the Republic, and although that same republic had become an empire it still made no difference. Either way, he still served Palatine who had access to powers he needed; he would do anything to learn those skills. If this was the price, then so be it. It had been easier to kill Kenobi than Dooku; After beheading the helpless Sith lord in accordance with Palpatine's command, he had been deeply troubled for a few days after rescuing the chancellor. Now, Vader was disgusted by Anakin's guilt. Palatine had only been trying to make him strong so he would be able to help Padme; what good was Dooku's continued existence in that equation? Palpatine's early teachings included the fact that the Dark side became more powerful and receptive to the users wishes the more often it was unleashed. Now that Vader knew how to use the dark power to his advantage, Kenobi's death did not bother him in the slightest.
Vader became aware that Padme still needed him. He would leave his Jedi starfighter on Mustafar and personally take Padme back to Coruscant for medical care. There was no point in retrieving Kenobi's body for Sidious (most likely his new master would chastise Vader's foolish sentimentality), but Vader felt that his former mentor deserved the cremation rituals of a Jedi funeral. Unfortunately, there was no facility available for the task on Mustafar. Vader resolved to do the next best thing; with the aid of the force, he lifted Kenobi's body out over the lava flow and dropped it in, where it instantly caught fire. The master's body lingered for only a second before the lava engulfed it and reduced it to ashes that became indistinguishable from the rest of the fiery flow.
“Goodbye, my old master.” Vader did not waste a second glance as he walked back to the ship where Padme awaited him.

Part II: Coruscant

Also, you use a lot of technical terms for stances and movements. Someone who doesnt know what those moves and styles mean would not be able to fully understand what you are trying to convey for the scene.

Show, don't tell.

Also, you should pick a viewpoint and stick with it. You're showing us what Vader felt and what Obi felt - this isn't exactly bad; it just means you're using the third person omniscient viewpoint, which probably isn't what you want. Pick just on of them, and don't tell us what the other one feels.

My only complaint: Don't use Kenobi over and over and over. Use Obi-Wan sometimes, or don't use names at all. It stutters the reading.

Great overall though.