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Rise of the Ronin has many characters you can form Bonds with throughout your journey. These characters can join you in combat, teach you new Combat Styles, and grant rewards for increasing your Bond with them. Some of them are even romanceable!
The easiest way to increase your Bond with these characters is to do their Bond Missions, special Side Quests that progress your Bond with that character. Bond Missions are only available during specific story chapters, but if you miss one, don't worry. You can always play ones you've missed (or replay ones you've already done) using the Testament of the Soul.