Instructions
Go to the fork in the road on the "World Map" screen of Melee Island. Wait for a pirate to approach you.
Select the "My name is Guybrush Threepwood. Prepare to die!" conversation option to start a duel with the pirate.
Trade insults and comebacks back and forth while you duel the pirate. Learn as many insults as possible before the fight ends.
Wait at the fork in the road for another pirate to fight. Fight as many pirates as is necessary to learn all 16 possible insults and unlock the "Sharp Tongue" achievement.