In Valor Mortis, upgrading your melee weapons takes Blade Materials, and they come in four tiers: Crude, Pure, Distilled and Quintessential. The first three take a weapon up to its base, upper and advanced levels, but to push a melee weapon to its highest level you need the rarest of them all: Quintessential Blade Material.
There are only 3 Quintessential Blade Materials in the whole game, and you will not come across any of them until the later regions: one is in The Outskirts and two are in the Fortress, the last of which is locked away in a secret room that only opens once you have defeated all 7 Eternal Guards. Upgrading a single melee weapon to its maximum level also unlocks the “Bladesmith” Trophy/Achievement.
This guide lists the location of every Quintessential Blade Material, so you can grab each one as soon as you reach its area and get your favourite weapon to full power.
Quintessential Blade Material 1
The first Quintessential Blade Material can be found in a chest near the "Lighthouse" Lantern in The Outskirts region.
The Quintessential Blade Material is a chest in the underground of the lighthouse, in the room where you fought the Experiment 83 Boss.
Quintessential Blade Material 2
The second Quintessential Blade Material is found in a chest down in the sewers below the "Ramparts" Lantern in the Fortress region.
From the Ramparts Lantern, backtrack into the room with the blue pole you can swing across to reach the door on the left.
Through this door, crawl under the web and go down the stairs, then go into the green room on the right where you will find the chest containing the Quintessential Blade Material.
Quintessential Blade Material 3
The final Quintessential Blade Material is locked away in the secret room near the "Courtyard" Lantern in the Fortress region, and you can only get in once you have defeated all 7 Eternal Guards.
Starting from the "Courtyard" Lantern, go into the main building on the left that has the big long hall. Inside, go all the way to the right where you will see the Eternal Guards symbol on the wall next to a hidden door.
To interact with the symbol you need all 7 Mysterious Stone Pyramids (dropped by the Eternal Guards mini-bosses). Once you have them all, they combine into the Mysterious Stone Slab, which you can use on the Symbol to open the secret room, where you will find the Quintessential Blade Material in a chest on the right.