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