Here is the full list of all 15 Nightingale achievements.
Visit The Watch
Complete the Quest "The Only Way Out Is Through"
Complete the Quest "Gateway to the Watch"
Complete the Quest "Eoten Offering"
Complete the Quest "Redress to the Sun"
Complete the Hunt Site of Power
Visit the Abeyance Realm
Complete the Gloom Site of Power
Complete the Herbarium Site of Power
Complete the Quest "Arm Yourself"
Complete the Provisioner Site of Power
Complete the Astrolabe Site of Power
Complete the Quest "A Realmwalker's Initiation"
Complete the Antiquarian Site of Power
Complete the Quest "Gift for a Gardener"