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