Part III: Three Sheets to the Wind
The first step is to defeat the pirates. Hagas asks you if you want help with the naval battles or not. With help, the ships will be defeated after getting hit with a single volley of cannonballs. Without help, you'll have to shoot your rivals several times before you can board their vessel. There's no impact on the game, so just pick whichever you want.
At any rate, look at the map on the table. Take your ship over to a pirate ship and you engage in battle. Once you win the naval battle you get to sword fight. Even if you lose to the pirate in the sword fight, you don't have to beat his ship again.
Rottingham explained the basics of insult swordfighting, and the gist is that you need to learn various insults and rhyming retorts. To learn both, you need to engage in a fight after you board a defeated pirate ship. You'll go first, so just pick whatever insult you want to kick things off. If the pirate knows the proper retort, then you'll learn it. Whoever uses the correct retort scores a point and is next to insult. The first one to three points wins the match.
After you win a sword fight, and plunder their treasure, use the map to head back to Puerto Pollo. Talk to Kenny and trade in your booty for the next model of cannon.
Keep fighting pirates until you have a large number of insults/witty comebacks stored up, then face Rottingham. Beat him in both areas of combat and you get your map back!
Check out the Insult List if you're having trouble winning.
