Some TMNT stuff really isn't for little kids.
In the published since 2011 IDW comic version of TMNT the backstory is modified in the respect of Splinter and the Turtles to the extent that they are all reincarnations of Hamato Yoshi and his four sons. Tang Shen was the wife of Hamato Yoshi, a member of the Foot Clan in feudal Japan.
When Yoshi was marked for treason by Oroku Saki, the leader of the ninja Foot Clan, after Yoshi openly criticized Saki's unnecessary blood thirst and increasing hunger for power. Saki had Tang Shen murdered by two Foot Ninjas, but Yoshi returned home just in time, to protect their children from the murderous thirst of Saki. Her dying words encouraged Yoshi to take their four sons and run. The dying Shen made her husband promise to not confront Saki in a fight, but to remain alive for their sons. Yoshi kept that oath, and he managed to hide for almost three years until they all were eventually tracked down and killed by Saki.
Since then, Splinter has revealed to the Turtles the story of his former life. Leonardo sometimes dreamed of Tang Shen, which for him was a confirmation of this story. Leonardo later turned against his family, by the magical brainwashing of the witch Kitsune, Tang Shen's spirit appeared and helped him (and Splinter) to make it back to his family.
She also appeared after Donatello was savagely beaten almost to death by Rocksteady and Bebop. She gave him some advice, and assured her son that whether he chose to live or die, he wouldn't be alone.