Lone Wolf and Cub: Sword of Vengeance

Set in Japan during an unspecific year of the Edo period, Ogami Itto, disgraced former executioner, or Kogi Kaishakunin, to the shogun, wanders the countryside, pushing a baby cart with his 3-year-old son Daigoro inside. A banner hangs off his back. "Ogami: Suiouryo technique" (Child and expertise for rent), it says. His services are asked for in a most unexpected way, when an insane woman seizes Daigoro from the cart and proceeds to try and breastfeed the boy. Daigoro at first hesitates, but after stern look from his father, he proceeds to suckle the crazy woman's breast. The woman's mother then apologizes for her daughter's behavior and tries to give Itto money, but the stoic ronin refuses, saying his son was hungry anyway.As he walks in the rain, he remembers another rainy day several months earlier when his wife, Asami, was slain by three ninjas, ostensibly in revenge for Itto's execution of a boy daimyo in the opening scene, but it was really part of a complicated plot by the shogun's Inspector Bizen and the "Shadow" shogun of the Yagyu Clan to frame Itto for treason and take over the executioner's post. Itto takes on Bizen and his men killing them all.Now a wandering assassin for hire, Itto takes a job from a local chamberlain, to kill a rival and his gang of henchmen, who pose a threat to the chamberlain's lord. The chamberlain plans to test Itto, but a quick slash behind his back with his Dotanuki sword dispatches the chamberlain's two men. The targets are in a remote mountain village that is home to hot-spring spa pools.As Itto pushes the baby cart, and Daigoro observes scenes of nature, such as a mother dog suckling one puppy, and two children singing a song and bouncing a ball, Itto thinks back again to the time just after his wife was killed. He gave Daigoro a choice between a toy ball or the sword. If the child chose the ball, Itto would put him to death send him to be with his mother (a better place in his opinion). But the curious child reaches for the sword; he has chosen to take the path of the ronin with his father, to live like demons at the crossroads to hell.Flashing forward to the present, Itto reaches the hot-spring village. He finds that the rival chamberlain and his men have hired a band of ronins who have taken over the town and are raping, looting and pillaging. Itto is forced to give up his sword and take his place as a hostage in the village.The ronins discuss killing Itto, but then decide to let him live if he will have sex with the town's remaining prostitute while they watch. The prostitute refuses to have any part in it, but then she's threatened by one of the men, a knife-throwing expert, and in order to save the woman, Itto steps forward and disrobes, saying he will do the men's bidding with the woman.In yet another flashback it shows the dramatic beheading and blood-spurting scene in which Itto defeats one of Yagyu Retsudo's best swordsman, with the aid of a mirror on Daigoro's forehead to reflect the sun into the swordsman's eyes.And then there is the big showdown in the village, where it is revealed that the baby cart harbors some secrets various edged weapons, including a spear-like naginata, which Itto uses to take out the evil chamberlain's men, chopping one off at his ankles, leaving the bloody stumps of his feet still standing on the ground.One of the men has matchlock pistols, but Itto quickly upturns the baby cart, which is revealed to be armored underneath, and when the gunman's pistols are empty, Itto quickly leaps over the baby cart and brings his blade down on the man's forehead, splitting it two.After all the enemy ronin are dead, Itto leaves the village, and the prostitute hopes to follow, but Itto makes a motion to cut the ropes on the bridge leading to town, to stop her from following, for the journey he is on is one that is for only him and Daigoro to make.

Question: Who takes on Bizen and his men, killing them all?
Answer: Ogami Itto