Phoenix:
Begin the quest by talk to Kumo in Leafre. He’ll ask you to find a Mysterious Egg.
Head to Cave of Trial 3 in El Nath and find for the mysterious egg in a hidden map.
Travel back to Leafre and talk to Kumo
Go left of Riprey and down to the map just before the hunting grounds for Sheep.
Enter the specified portal. Drop the egg in a specified location, which will summon a Phoenix. Kill it.
Once your done return to Kumo. He will give you the skillbook for Phoenix.