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Description: Complete 100 percent of the Vigils in the Memorial.

How to Earn: After you have gotten so far into the story you'll be able to build a Memorial and later you will be able to upgrade it to unlock all 23 vigils. Each vigil is essentially a challenge to complete. When you complete a challenge you will receive an inventory item specific to that challenge. Take the item to the Memorial and select the vigil with a red star over it to "complete" the challenge.

I recommend completing the vigils in your first playthrough. Once you have completed the game for the first time select "Continue" from the Main Menu to load your game just before the last level. You can then use "Who Knows Where" for the weapon ones as well as the proving grounds.

The only thing I would add that is not in the guide... The Proving Ground for the Flaming Bellows is also very easy if you have 3 or 4 upgrades on it. TSG Dwaggie comments that rolling after each of the first two groups of enemies will make things even easier.
The proving grounds I completed (and found the easiest were):
Bow, Repeater, Musket, Hammer, Flamethrower, Mortar, and Pistols.