To unlock the Shroomtender Hat, you need to complete the Necrom Grand Adventurer achievement. This is a simple and easy achievement to unlock, it's just time consuming.
You need to complete 28 unique quests in the Telvanni Peninsula and/or Apocrypha zones to finish this. That means pretty much any quests that are not repeatable, for example daily quests do not count towards this achievement, but any of the Necrom main quests or side quests in those zones will count towards it.
Once you finish the achievement, you'll immediately unlock the Shroomtender Hat.
