You can increase your attack power by surrendering Battle Memories to any Sculptor’s Idol. These are dropped by major bosses, the first one you’ll get it from is by defeating Gyobou Oniwa in Ashina Castle (or from Lady Butterfly in Hirata Estate, if you're crazy and skillful enough to face her early on). Once you have the battle memory, commune with any Sculptor’s Idol and select Enhance Attack Power.
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