This page of our guide to Ghost of Tsushima has a description of the boss fight with The Spirit of Yarikawa - she appears in The Spirit of Yarikawa's Vengeance side quest.
The Spirit of Yarikawa will attack you when you reach the place indicated on the map. This is the last part of this mission. When you beat your opponent, you will get a reward and experience points.
The Spirit of Yarikawa isn't a difficult opponent. All you have to do is dodge her attacks. Pay attention to how your enemy acts - she mainly protects herself against your attacks rather than trying to attack you.
A good strategy is to attack her in rapid succession. That way you will have a chance to weaken the enemy and take a lot of health points.
The Spirit of Yarikawa, however, can take advantage of your lack of attention. If you turn your back on her or let your guard down for a while, she will attack. Defend against her attacks and then go into the offensive.
An interesting note about this fight is that even though you are being watched by other people, you are unable to harm them. They are passive observers who do not react in any way to the ongoing duel.