The Four Fierce Axes quest is likely the second you'll acquire in Phantom Blade Zero, after Flesh Lily, when you find a "Four Axes" case file in the Broken Puppet Valley early on.
You'll have to "uncover the truth behind the Four Axes Rebellion" which involves continuing to the outpost and defeating the Peng Meng boss there. After that, you'll have to "gather evidence of the conspiracy against the Four Axes", which means finding seven more "Four Axes" case files in Weeping Creek Valley, besides the one you already have and one Peng Meng drops. Here's where they all are:
