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
COMPLETE SECOND RUN
COMPLETE THE GAME
COMPLETE THE GAME WITH 100% OF THE ITEMS, COINS, AND HEARTS
COMPLETE THE GAME WITHOUT KILLING ANY SNAKES
FIND ALL ITEMS
FIND ALL HEARTS
SOLVE ALL TEMPLE PUZZLES
FIND ALL COINS
FIND ALL TENTACLES
SHUT DOWN THE SWORD FACTORY
FIND ALL HOTEL GUESTS
TALK TO MARY
BRING A GIFT TO THE DOG
USE ALL TELEVATORS
FIND AND DEFEAT THE OASIS GHOST
USE A TELEVATOR
VISIT THE ISLAND
FIND YOUR FIRST TENTACLE
UNLOCK A NEW HOME
PLAY SOME REAL MUSIC
FIND YOUR FIRST HEART
WATER THE DOG
FIND YOUR FIRST COIN
FIND AN ITEM, COIN, OR HEART WITH LESS THAN 1 SECOND LEFT
LET THE OLD PERSON FINISH TALKING
FIND YOUR FIRST ITEM