Here is the full list of all 27 MINIT achievements worth 1,000 gamerscore. It takes around 2-3 hours to unlock all of the achievements on Xbox One.
FIND AN ITEM, COIN, OR HEART WITH LESS THAN 1 SECOND LEFT
BRING A GIFT TO THE DOG
USE ALL TELEVATORS
LISTEN TO THE OLD PERSON
WATER THE DOG
FIND YOUR FIRST COIN
USE A TELEVATOR
VISIT THE ISLAND
FIND YOUR FIRST TENTACLE
UNLOCK A NEW HOME
PLAY SOME REAL MUSIC
FIND YOUR FIRST HEART
FIND YOUR FIRST ITEM
FIND ALL ITEMS
FIND ALL COINS
FIND ALL HEARTS
FIND ALL TENTACLES
SOLVE ALL THE PUZZLES IN THE SECRET TEMPLE
FIND AND DEFEAT THE OASIS GHOST
FIND ALL HOTEL GUESTS
TALK TO MARY
SHUT DOWN THE SWORD FACTORY
COMPLETE THE GAME
COMPLETE SECOND RUN
COMPLETE THE GAME WITH 100% OF THE ITEMS, COINS, AND HEARTS
COMPLETE THE GAME WITHOUT KILLING ANY SNAKES
COMPLETE THE GAME IN 25 RUNS OR LESS