When you first talk to the Fisherman in Pilgrims Passage he’ll ask you to catch him a lobster, a squid, a octopus, and a crab. I recommend using the Ritual of the Ocean’s Bounty to help you catch these. For each one you catch he’ll give you one of four pieces towards unlocking a fleece.
Soz will ask you to give him Menticide Mushrooms and do some other tasks all in all you’ll need about 65 Menticide Mushrooms. I recommend you grow these yourself using the spores you can find. Do all of his tasks and he’ll give you all the pieces for your next fleece.
Plimbo will ask you to get Witness eyes. You can find these by getting to the boss room in a dungeon where you have already taken out the main boss. Do this once per dungeon and you will get all the parts you need for another fleece.
Midas will give a piece for every follower you give him up to 4. The spot where you sacrifice them is in the northern part of his lair as seen in the photo.
The wolf man as im going to call him can be summoned at 4 locations but only during the night. each time he will ask for something and in exchange he will give you one piece. There is one in Pilgrims Passage, one in Smugglers Sanctuary, one in Midas’s cave, and one in the spore grotto.