For this mission walkthrough in Red Dead Redemption, follow the point on the map labeled Marshal Johnson. Bonnie advised you to meet and talk, as she believes the Marshal can help with the bandit Bill Williamson.
Enter the building and watch the cutscene. The Marshal will tell you that conducting any operations against the bandit is not within his jurisdiction and will refuse to help. However, the hero manages to strike a deal: you help the Marshal with troublemakers in the saloon, and he helps you with Bill. Follow Johnson to the saloon. The first people you will have to deal with are a gang led by Walton — road agents who prey on the town. You will need to follow Walton, who has just left for his hideout on horseback. To call your steed, use a whistle. Note: Be careful before using your weapon, as Walton must not be killed! Upon arriving at the Old Pleasance House, the armed men will open fire. Take cover behind the broken cart in front of you and shoot back at the bandit's men.
After numerous killings, you will find that Walton has escaped. From this point on, your task is to catch him either alive by shooting at his legs or dead. Just then, he will come out of the building he was hiding in. Shoot him then. Upon completing this mission, you will receive +37 points in the Fame category and -50 points in the Honor category. This means that dishonorable people will react positively if you have a low reputation, while honorable people will react negatively. Head back to town. On the way, in the desert, you will notice scoundrels robbing a treasure hunter.
Kill them and talk to the hunter. He will give you a treasure map as a token of gratitude.