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