Hell's Pavement
Davy Jones
Sailor slang for death at sea—the ocean floor is "Davy Jones's locker." Billy's swearing off the sea means swearing off dying young.
copper-bound official
The ship's paymaster, called "copper-bound" because he's bureaucratic and rigid—or because he handles copper coins. Either way, he's just doing paperwork while Billy's about to blow his wages.
painted the alongshore blue
Sailor slang for a drinking binge in port. "Alongshore" means the waterfront bars and brothels. Blue = drunk, profane, or both.
So he did
The refrain switches from his promises ("So he said") to reality ("So he did"). The poem's whole structure is promise vs. outcome.