Here is the full list of all 28 Minit trophies - there are 8 bronze, 14 silver, 5 gold and 1 platinum.
UNLOCK ALL OTHER TROPHIES
COMPLETE THE GAME IN 25 RUNS OR LESS
PLAY SOME REAL MUSIC
COMPLETE SECOND RUN
COMPLETE THE GAME WITH 100% OF THE ITEMS, COINS, AND HEARTS
COMPLETE THE GAME WITHOUT KILLING ANY SNAKES
COMPLETE THE GAME
FIND ALL ITEMS
TALK TO MARY
FIND ALL HEARTS
FIND ALL COINS
SOLVE ALL TEMPLE PUZZLES
FIND YOUR FIRST HEART
FIND ALL TENTACLES
USE ALL TELEVATORS
BRING A GIFT TO THE DOG
LET THE OLD PERSON FINISH TALKING
USE A TELEVATOR
VISIT THE ISLAND
WATER THE DOG
FIND AN ITEM, COIN, OR HEART WITH LESS THAN 1 SECOND LEFT
FIND YOUR FIRST COIN
SHUT DOWN THE SWORD FACTORY
FIND YOUR FIRST TENTACLE
FIND ALL HOTEL GUESTS
FIND AND DEFEAT THE OASIS GHOST
UNLOCK A NEW HOME
FIND YOUR FIRST ITEM