Upgrading medicine in Phantom Blade Zero improves the percentage of HP, damage negation, and Sha-Chi that these healing consumables replenish, which is pretty powerful, as you'd imagine.
You can upgrade your medicine when you reach the Green Serpent House in west Pangzhen (the game's 4th region after the Village of Lu). You'll arrive at this location during Pangzhen's second chapter, which sees you exploring the west side of the town, specifically, after you defeat Xie Qiudong, The Divine Healer and progress down the street, where you'll spot a big house with green banners and the Green Serpent House bell.
The Apprentice Healer here will upgrade your medicine using Apprentice Healer's Memories and Skilled Healer's Memories, some of which you likely will have already picked up during your explorations. You'll also get the Green Serpent Brew medicine, which removes status effects, when you visit for the first time.
