Here is the full list of all 39 Return to Monkey Island achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Found Cogg Island
Performed The Ole Switcheroo With The Replica Flag
Explored The Entire Ocean Floor
Let The Lumpsucker Escape
Got Hired With All Four Mop Heads
Braved The Scorched Alaska
Reached The End In 2 Hours Or Less
Returned To The World You Know
Did Gullet A Favor
Offered To Donate To The Earthquake Relief
Got To The Heart Of The Problem
Listed Every Mess On The First Swab’s Report
Attempted To Steal The Cook’s Mop
Rescued Wally From Monkey Island
Found All The Copies of ‘At The End Of The Plank’
Died For Real
Gave Stan His Toothbrush
Waited Patiently To See Carla
Decked Out The Sea Monkey II With Spooky Skulls
Answered One Hundred Trivia Questions Correctly
Told Everyone On Mêlée Island That You Are Looking For The Secret
Thoroughly Examined All Of Wally’s Stock
Shared Your Luck
Started Part Five
Answered Seventy-Five Trivia Questions Correctly
Became A Prize Chum
Answered Fifty Trivia Questions Correctly
Ahoy! More Than Twenty Times
Started Part Four
Answered Twenty-Five Trivia Questions Correctly
Started Part Three
Answered Ten Trivia Questions Correctly
Collected More Than Twenty Trivia Cards
Swabbed The Hold Twenty Times
Started Part Two
Freed Otis
Convinced Cobb To Tell You About LOOM
Started Part One
Fulfilled Your Restroom Obligations