You know the number 2 killer of pirates? Scurvy. The cook on Captain Scarlett's ship needs some help in keeping the crew alive long enough to die from the number 1 cause of death, self inflicted gunshot wounds. You can get this mission from the bounty board on the ship after completing "A Study in Scarlett".
|Normal||True Vault Hunter|
After picking up this mission, go back west and you'll find a pirate camp by where you entered Wurmwater. You might have to fight your way into the camp a little ways but your targets are the melons hanging from the large palm trees. Simply shoot them off and grab them. Don't worry if they break because the tree will make more. In fact, it happens fast enough that you only really have to find one tree.
Be careful though as this is a semi-large pirate camp. It may be to your benefit to kill as many pirates as you can to protect yourself. In fact, this is the same camp where you find "Message in a bottle 2" and that's on the far side of the camp so you could also grab both missions at the same time.
When you've gotten 20 melons, take them back to the bounty board on Captain Scarlett's ship for your reward.