The Sword of Tengu was an electric sword created by Ch'rell.
When Ch'rell took up the mantle of the Shredder, he had some sword smiths craft the sword out of Utrom metal. When sword was finished, the Shredder made a tale of "how it fell from the heavens" and "was crafted by the goblins.". He used the sword to kill its makers.
Ch'rell used the sword to subjagate Japan and brought the Tokugawa Clan to power. Somehow, he lost the sword and the sword remained lost for centuries. The sword ended up in a museum within New York. The Shredder sent his Foot ninjas to bring back the Sword of Tengu. They got the sword and Hun presented it to the Shredder. The Shredder told Hun to have two Foot technicians to use it as a component for the sonic cannon to retrieve the Utrom exo-suit which they managed to get but the Turtles got the Sword of Tengu and kept it in their lair.
Leo carries the Sword of Tengu which he, his brothers, and Splinter think it might be useful to fight against the Shredder.
Splinter used the Sword of Tengu to defeat the Foot Mystics but got his hands burned in the process. He told his sons that a true Ninjustu master could hold the sword without a protective glove but at the cost of his hands getting burned.
Leo uses the sword to save Don from the Shredder's wrath and blasted the Shredder into a pond. The Shredder crawls out of the pond and decides that he cannot be defeated. He presses a button which summons a group of Foot ninjas piloting Razor Jets. The Turtles see them, and the Foot ninjas begin firing at them. A Razor Jet pilot fires at Leo which made him drop the Sword of Tengu. Leonardo confronts the Shredder who calls upon the Foot Elite to finish to fight Leo. The Shredder tries to grab the sword while Leo fights the Elite guards but Donatello shoots down a Razor Jet which sends the the Razor Jet to crash into the spot where the Sword of Tengu was. Saki tries dig through the wreckage to find the sword. Leo confronts the Shredder again but he summons more Foot ninjas. The Guardians arrived and faced the Foot ninjas while the Turtles fight the Shredder. Saki managed to find the sword and grabs the sword which made him more powerful. He fights the Turtles with the sword but the Turtles managed to get the sword out of his hand, sending it in midair. Donatello throws the protective glove to Leo and Leo catches the glove and the sword. Leonardo confronts the Shredder who retrieved Leo's katanas. The two adversaries begin gazing and jumped into action. The Shredder was decaptited by Leo who was unaware that the Shredder is an Utrom and the head was robotic at that time. After the fight, Leo used the Sword of Tengu with Stockman's robotic arm (Leo chopped it off earlier before) to destroy the systems in the Foot HQ which destroyed the robotic arm and the sword in the process.