How to Find Blackguard Big Boggart and Complete His Quest

First Meeting - Boilprawn Shack: Blackguard, initially known as Blackguard, is found at Boilprawn Shack, southwest of Academy Gate Town Site of Grace in Liurnia. Rya will send you to retrieve a stolen necklace from him. You can either buy the necklace for 1000 Runes or kill him and loot it. To progress his quest, buy the necklace. This also unlocks his shop, where he sells Boiled Prawn (a consumable that boosts physical negation). Purchasing an item establishes a friendship, allowing you to summon him for the Magma Wyrm Makar boss fight in the Ruin-Strewn Precipice.

Second Meeting - Leyndell, Capital Outskirts: After reaching Altus Plateau, head northeast to the Capital Outskirts. From the Capital Rampart Site of Grace, go northeast and follow the path down to the water. Blackguard will be camped to the west. Speak with him; he now sells Boiled Crabs (an improved version of Boiled Prawns). Exhaust his dialogue, and he will warn you about the Dung Eater, mentioning his past in prison together.

Final Meeting - Leyndell, Capital Outskirts: Progress the Dung Eater's Quest until he mentions waiting in the outer moat. Return to Blackguard and exhaust his dialogue. He will believe the Dung Eater is nearby. Refresh the area, and you will find a wounded Blackguard who asks for death. Grant his wish to obtain a Seedbed Curse, Blackguard's Bell Bearing, Iron Ball, and Blackguard's Iron Mask. You will then be invaded by the Dung Eater; defeat him to obtain the Sword of Milos and progress his quest.