Here is the full list of all 41 Castaway Paradise trophies - there are 18 bronze, 21 silver, 1 gold and 1 platinum.
Grow every type of crop
Harvest 50 crops
Collect 25 pieces of garbage
Rebuild Francis' Pirateshack
Rebuild Amelia's Planehouse
Changed every piece of outfit
Wore an outfit of the opposite gender
Live the luxury life of a VIP
Donate 15 bugs
Used every piece of equipment
Rebuild Angus' Trailer
Donate a collectable
Rebuild Harold's Museum
Rebuild a bridge
Unlock the second room in your house
Remove 25 stones
Completed 25 quests
Rebuild Gustave's Bakery
Get your first collectable
Completed the tutorial
Got all trophies
Donate all fish
Donate all bugs
Donate all shells
Donated every collectable
Introduced yourself to all the villagers
Visit all buildings and rooms
Rebuild Victoria's Mansion
Rebuild the Lighthouse
Unlocked a gate
Grow every type of fruit
Grow every type of flower
Donate 15 fish
Donate 15 shells
Read 50 chit chats
Completed 100 quests
Make a profit of 500 gems on the Stock Market
Make a profit of 5000 gems on the Stock Market
Make a profit of 2000 gems at the Bank
Remove 50 weeds
Remove 25 cobwebs