Trade 6 elemental crystals or 2 light/dark crystals to unlock this mission.
After accepting the mission from a Gate Guard, speak to Tosuka-Porika at the Optistery in Northern Windurst Waters (G-8) for a cutscene. He will give you the Optistery Ring (temporary key item). NPCs inside both buildings of the Opistery have additional dialogue.
Travel to Toraimarai Canal and go to (G-8) (Second Map). There is a large room with 4 Hinge Oils accompanied by few bats.. The bats are aggressive towards level 75 characters and the oils will link, if within range.
Using the Home Point tele will place you in front of the Full Moon Fountain entrance on the 1st map, where you can make your way to exit C leading to the 2nd map.
Entering the canals from Windurst Walls will also place you a short distance away so it really doesn't matter which way you take.
The re-spawn time for the Hinge Oils is 16 minutes. All 4 must be defeated in order for you to enter the Animastery through the Marble Door on the far side of the room, up a staircase at (H-8). If even one of the oils re-spawn before you click the Marble Door, it will be "locked" until all oils are defeated again.
They have a very nasty, but short-range (less than 10'), AoEFluid Spread that can tear through mages.
The stack of books that you have to examine for the mission is on the floor, to the left of the Marble Door from which you entered. The other Tomes of Magic on the walls holds some interesting information, but are not part of the mission. You will know you have the right "Tome of Magic" when a cutscene starts.