Some TMNT stuff really isn't for little kids.
A pair of ninja members of the Foot Clan, Oroku Nagi and Hamato Yoshi, had both competed for the love of a woman named Tang Shen. However, Shen only loved Yoshi, which enraged Nagi. Nagi attacked Shen, and in her defense, Yoshi attacked and killed Nagi.
Disgraced for killing another member of the Foot Clan, Hamato Yoshi fled from Japan to the United States with Tang Shen and his pet rat, Splinter. However, Nagi's younger brother, Saki, swore revenge on his older brother's murderer.
He eventually tracked down and killed both Hamato Yoshi and Tang Shen. Joining the Foot Clan himself and trained to be a ninja, Saki quickly rose through the ranks, and was put in charge of the American branch of the Clan. Under Saki's leadership, The Foot participated in a variety of criminal activities, including drug smuggling, arms running, and assassination. This also allowed him to finally move to New York City to avenge his brother’s death by killing Yoshi and Shen; however, Yoshi’s pet rat Splinter escaped and later mutated into an anthropomorphic form, and spent years training the four turtles to avenge Yoshi and Shen.
Fifteen years later Oroku Saki was seen now running a protection racket. When Splinter felt the Turtles were ready, he asked them to challenge and kill Oroku Saki. This first fight took place at night on a rooftop in New York City. After a bloody rooftop battle, Leonardo managed to run him through with his sword. Allowing Shredder to commit seppuku, thus dying an honorable death, he instead opted to throw a thermite grenade at them, in an attempt to take them with him to his death, which Donatello would bat back at his face. The explosion as well as Shredder falling off the rooftops would be the end of him. With their leader dead, the Foot would continue to hunt for Splinter and his turtles in revenge.
Some time after the death of Saki, Shredder and the Foot Clan would attack Leonardo during a training session on a rooftop. It was revealed later that this was a worm colony clone of Saki. It retained all of Saki's memories, due to the Foot Mystics attempts to revive Shredder. Sometime later the clone became a shark mutant with vengeance against the turtles, who eventually ended the Shredder for good.
Due to Shredder's death, the Foot would still be after the turtles. The Elite Foot in particular were after Leo's head. The TMNT would be forced to help Karai (leader of the Japanese branch of the Foot who came to New York City) kill off the Foot factions that were battling each other in exchange for a truce. And sure enough, after they defeated the Elite, Karai and the Foot promised to leave the Turtles alone.
So even after Shredder was only fought with and killed off in one day, his shadow continued to haunt the Turtles for years to come, be it in the form of worm clones, the rest of his clan or Karai.
This version of the Shredder had made a brief cameo in the movie Turtles Forever, playing the same role he did in Volume 1. He appeared to the Mirage Turtles to challenge them when the 1987 and 2003 Turtles threw trash cans and assorted garbage at him causing him to fall off the ledge of the building.