Most chests in one place are in Leviathan's Lair - 14 of them, countung the one in secret chamber.
Leviathan's treasure room is accessible twice during the questline, plus there is a glitch to break into it later. There are hosts of instructions on Youtube, but I've found this one to be the easiest.
I'm about to start a second playthrough of Captain Scarlett, and will try to mark down all chests I find. If anyone has that information, let's work together!
- 1 chest on the refinery supports, to be jumped to from a moving elevator.
- 2 chests near vending machines in the middle of the map, in the water under a rock.
- 1 chest after Sandman, on the right.
- 1 chest in the middle of first large shantytown ship you go through.
- 1 chest in top end of the second large shantytown ship, behind a shack.
- 1 chest on the last ship in the center of the map, right at the turret on the deck.
- 1 chest a little past the H3RL-E's lair.
- 1 chest in a secret room above the Arm (jump across the drop when returning from H3RL-E).
- 1 chest on a wooden platform under a house near Maroonie's Secret Stash.
- 2 chests atop the lighthouse itself.
- 14 chests in the treasure room. See glitch.