Here is the full list of all 17 Stay Close achievements.
Finish the Game in 30 Minutes
Win 10 SP games
Win 10 Coop Games
Fulfill Cyrus' game
Find the key
Find them
Find the compass
Find the supporter wall
Find Cyrus
Don't get caught by a Creeper
Finish the Game without dying
Win one SP game
Win one Coop Game
Read all notes
Find Emperor Olaf
Find Jeeny
Find Maya