Catching the Griffin soul in Forsaken World is very similar to the Nightmare soul. Only difference is the location and the griffin’s level.
Head over to Hazed Wilderness, more appropriately to the area north of Hall of Mist. You can either teleport to Kindling Encampment or use some shortcut. The reason I mentioned the shortcut because it makes sense to hunt for the Griffin soul the same time when you hunt for the Nightmare. Now if you do that, and you really should, when you use your flying mount it is only a short trip from Lunagrant to Hazed and back.
The Griffin is wandering in the area show on this map
It has the same 4 hour respawn time but it is higher level than the Nightmare. It’s lvl 60 so if you try to do it efficiently and hunt for them at the same time, make sure you are at an appropriate level for both. If the griffin is too much work for you at your level, stick with the Nightmare until you level up some.
How to catch the Griffin Soul
Same method as mentioned at the Nightmare. Bring its HP down to 50% and use your Advance Soul Catching. Watch out for competition because the soul is up for grabs.