Lone Wolf and Cub: Baby Cart in Peril

In this fourth 'Lone Wolf and Baby Cart' movie we are introduced to Oyuki, a tattooed female assassin and the renegade member of a daimyo's personal bodyguard detail who is killing every man that is sent up against her. Along with her deadly use of the short blade, she strips to the waist while fighting to reveal elaborate tattoos on her chest and back. On her front is a kintar grasping her left breast. A portrait of a mountain witch covers her back. She then cuts off her victims' topknots, or chonmage, which brings dishonor to the dead man and his family.Ogami Itto, the disgraced former shogun's executioner, or Kogi Kaishakunin, is hired to kill Oyuki. He tracks down the tattoo artist, who explains that she was a "fine" woman who did not scream as he dug into her flesh with his needles.Meanwhile, Itto's 3-year-old son, Daigoro, has grown restless waiting by the baby cart his father uses to trundle him about in. He goes exploring and finds a pair of performing clowns on the street. When the clowns finish their performance, Daigoro follows them, hoping to see more. But the clowns shoo him away, saying it's time to go home. Now, Daigoro has wandered too far. He is lost, and has become separated from his father.Agents of the Ogamis' mortal enemies, the Yagyu, are never far away. A procession of them, accompanied by the sound of gongs and loud shrieks, sends Daigoro into hiding. Itto must give up his search rather than risk an entanglement with the men, so he travels on alone.Daigoro spends days looking for his father, searching in every temple in the countryside. He enters one temple and sees a figure at the altar praying, but it is not his father. Rather, it is a man whom Daigoro immediately recognizes as someone who is unfriendly.The man follows Daigoro, who wanders into a grass field as it is being lit on fire by farmers. Unwittingly, Daigoro is surrounded by the flames, but he proves his resourcefulness by burying himself and surviving.The man then turns his sword on Daigoro, who raises a stick to defend himself, and in that instant the man realizes who Daigoro is. Just then, Itto comes into the picture, and the two recognize each other. The man, it turns out is Gunbei Yagyu, the outcast son of Retsudo Yagyu (from the first 'Lone Wolf' movie). Gunbei and Itto had competed for the post of shogun's executioner, and Gunbei's fierce swordsmanship surely would have won him the post, but in his overzealousness, he ends up pointing his sword at the shogun a taboo movement that costs him the job and makes him an outcast.Itto and Gunbei now have a rematch, but Itto is much improved and is ready for Gunbei. With a swift stroke, he chops off Gunbei's right arm. Gunbei then begs Itto to kill him, but Itto refuses, saying there is nothing to be gained from slaying a man who is already dead.With Gunbei out of the way and father and son reunited, the action then turns on finding the tattooed killer, Oyuki. He first stops at a settlement of street actors that Oyuki was said to be a part of. He talks to the elder and hears more of her story, and it happens that the elder is Oyuki's father, who is opposed to her actions, and cooperates with Itto.Itto finally locates Oyuki at a hot spring and witnesses her in action against more vassals who have come to try and kill her. Then her arch nemesis, her former instructor who raped her and set her on her bloody vendetta, shows up with his flaming sword and blazing eyes. But she is no longer in his sway, and when he sees her tattoos, he is distracted and killed.Finally, Itto and Oyuki must duel, and he makes quick work of her. She dies a splendid death, as Itto says, without having to disrobe.Retsudo Yagyu, meanwhile, has been playing politics. He manipulates a local daimyo into bringing in Itto, but Itto is able to use the baby cart and its weapons to escape from the daimyo's palace and take the man hostage. As Itto is leaving the area with the daimyo along for safety, he is attacked by the Yagyu. The daimyo is killed by some musketeers and Itto goes headlong into battle, telling his son Daigoro that he is entering the "crossroads to hell." It is a fierce battle, ending with Itto and Retsudo in combat. They trade blows Retsudo gets a blade in his right eye and Itto a sword in his back. Itto kills the swordsman who stabs him, but Retsudo gets away.Daigoro finds his father and with great effort, pulls the sword from his father's back. Despite being severely wounded, Itto carries Daigoro to the cart and slowly pushes it away, seeking medical treatment for himself. Watching over the scene is the now one-armed Gunbei, who is happy to see Itto live to fight another day.

Question: Ogami Itto is hired to do what to Oyuki?
Answer: kill