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