The trophies are swapped, completing 'danger in the deep' will give you the 'distant shores' achievement. I'm playing on a ps4 save
GINGER ISLAND SPOILERS BELOW
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Once you've reached ginger Island and collected enough golden walnuts to enter the Walnut Room, you'll be able to access more quests (2 to choose from each week). Accept the 'danger in the deep' quest when it appears. It will change the regular mines to a difficult version and completing it gets you the 'danger in the deep' achievement. However, with the current bug, it will instead grant you the 'distant shores' achievement.
If you've already completed the quest, you do not have to redo it. Instead, go to floor 120 and set the shrine to the dangerous mines if not already activated. Return the next day and you should get it. This is how I got mine to work. Hope it helps :)