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