Here is the full list of all 37 Bilkins' Folly trophies - there are 19 bronze, 13 silver, 4 gold and 1 platinum.
Unlock all other trophies
Cause a seagull to crash into the camera
Find your first piece of junk
Reach Crabb Island
Collect 5 pieces of booty
8 pieces of junk
Reach Phelmy Island
Unlock the ship
Snag a fish
Mine a gold nugget
Reach Remy's Lott
32 pieces of junk
Collect 20 pieces of booty
Decide Philmore's fate
Reach Leeky Harbor
burgle every home in Leeky Harbor
Fully upgrade your ship
Beat the minecart puzzle
Reach Shattered Peak
Have a conversation with Rosemary
Beat the bats dungeon
Collect La Moina's key
Share an informative meal with the crew
Make amends with the boss of Remy's Lott
Solve all of Carlos' songs
beat the game without ever turning on normal mode
pat all the animals
find 64 pieces of junk
find every gold nugget
collect every piece of gear
Collect every last piece of booty
Fame or family - make a choice
catch every fish
find all the quest items, gold nuggets, pearls, booty, diary pages, junk and fish... phew!
Find a secret in Drayton's dream world
Come to a resolution with Gail
Have a conversation with Winston