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