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