DREDGE

Story-Related, Cannot be missed

The Twisted Strand is the northwestern swamp area of the map. A number of the livestock will need a Mangrove rod to be fished up, which you can make available in the Traveling Merchants shop through Research Parts on the Rod tab. You will need to have at least used two parts to unlock the Flexible Fishing Pole (Coastal/Shallow) which will allow you to unlock the Anti-Tangle Line (Mangrove/Coastal) for an additional two research parts, and the rod will cost you ~$350.

When you first arrive at the swamps of Twisted Strand, you can explore the area, but you will likely see the threat that is stalking the murky waters and the roots of the swamp plant life that seem to move around you and at times block your path. You will need to find the Marooned Airman amid the swamp and complete a set of quests for him.

First he will tell you of the Mind Suckers (yes, there are three of those creatures, not just one) and how his crew was eventually all taken by the beasts. He will then task you to gather the two pieces of his Mortar. The Mortar Barrel can be found at the right location (G13) and the Mortar Frame can be found at the left location (E14) in this image:

There will also be a side Pursuit to find the Dog Tags of the Airman's fallen companions. These tags will award you with Research Parts from the Airman when they are turned in, so make sure to do so before the last Mind Sucker is killed. Those can be found in the locations marked by crab pots (not the Xs) in this image (D12, E14, H13) 

Once the full Mortar is retrieved, the Airman will ask you to gather fish for bait.

Bait #1 will need:

Bait #2 will need: 

Bait #3 will need:

Once you have all three baits ready, it is time to fight back against the Mind Suckers.  Approach the three traps within the swamp and place the bait in each. Within seconds, the Mind Sucker will emerge and get caught in the trap. The Airman will shoot the Mortar and kill each of the three beasts. You will need to retireve the carcass of all three and bring them back to the Airman. Whichever carcass is given last to the Airman, it will reveal the Necklace Relic.

If this is the fourth relic you are turning in, then return to the Collector to receive the Atrophy ability which is useful for Aberration Attractor  as it guarantees one aberration on nearly every use, as well as finally awarding you this trophy.

Retrieval of the relic and all Twisted Strand Pursuits for the Providence  trophy can be found in the video below. Please take note that the information in the below video was made before Patch 1.1.0 was released. The timer has now been removed from the Hooded Figure Pursuits, so you should have an easier time succeeding on that Pursuit: