Just got Swaine, worth going back for the green
chest in DDD?
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Just hop on the boat. Most of those green chests are just gems to teach your familiar skills. Most of them aren't that good anyway. Wait until you can unlock the purple chests before going back for green chests so you can grab both at once.
And do horace's riddle side quests to get that skill to reveal where chests are in town and dungeons.