The side-quest can be activated by finding a message in a bottle. You have to find treasure chests scattered throughout your journey and some of them are really tricky to pin down.
Hopefully, this guide will help you track down every last one of them. Following is a location based guide starting from the town of Oasis:
Captain Scarlett and Her Pirate’s Booty Treasure Locations
Oasis Location. Go to the eastern side of the town fence, you will find an alley facing towards the north, go in the alley. There is only one shuttered door here with a green button, press the button and you will find the treasure inside.
Hayter’s Folly Location. Make your way to southwestern corner of the map. Jump off the bridge here and you will find some rocks you can climb around the waterfall.
Leap across the waterfall to the other side. There will be lots of rocks here and behind them a wall, look down facing the wall and examine carefully to find a bottle.
You can break this bottle and doing so reveals a secret room. Quickly finish off the enemies inside and look for an X in the back left corner to find the treasure.
The Rustyards Location. Go to the west end of the yards sticking close to the cliffside. Keep your eyes peeled for the worn down shacks littered with garbage. Inside one of them you will find the X. Interact with it to reveal the treasure.
Wurmwater Location. Make your way towards the centre of this area. You will see a canyon leading to the centre from the east. Here you will find an anchor. Near the anchor towards the left side is the X, interact with it to get the treasure.
Magnys Lighthouse Location. Find the lighthouse at the north of the map, here you will also find a tall row of rocks towards the north edge of the cliff. The rocks are impossible to climb from your current position so make your way to the top of the lighthouse.
Looking down you will see the rocks and you might have guessed what’s coming up next. Jump from the lighthouse aiming for the top of the rocks. If you make the jump you will find yourself next to the X.