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