This chapter is the shortest. You spend most of the time desperately wondering around the town looking for parts to make traps before the time runs out. These traps are supposed to eliminate the majority of a gang of ruffians so that you'll be able to battle their boss with ease. If you don't set up enough traps then there'll be too many bad guys to fight which results in losing.
Pro-Tip: Make sure to snag the rifles in the sheriff's office! One of them makes the blue guy quite powerful, especially when he uses his technique that makes him go ballistic and shoot everything around him. That helps a great deal in the last battle.

Note: The following screen shots are from an older version of Live-A-Live's English translation. The newer translation looks nicer!