Here is the full list of all 16 Jolly Rover achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Found all pieces of eight
Earned maximum score
3x coconut knock-out
Sent a shipmate on a trip to remember
Escape in a hot air balloon
Completed game without hints
Found all crackers
Defeated DeSilver
Rode a sea turtle
Found Silvereye's treasure
Found all pirate flags
Sailed to Shipwreck Island
Infiltrated pirate stockade
Joined a pirate crew
Invented the trampoline
Escaped Howell's Ship