For the Legendary Amulet from Seasons of the Dragon you do not need all Living World Achievements. Not even close. Getting "Aurora" (the LS3 trinket/earring) requires a lot more achievements, basically Mastery in all LS3 chapters. Same for "Vision" (the LS4 trinket/earring).

The only (maybe) annyoing thing about the amulet is that (depending on when you started) you may need to replay (many) Living World story chapters you completed before the Return to ... achievements have been added to the game.