Contract: The Creature From Oxenfurt Forest - Novigrad
Quest Giver: Oxenfurt Notice Board
Other Requirements: N/A
This quest can be started one of a few different ways, the most common is by grabbing the notice off the Oxenfurt Notice Board. You could also speak with Hans of Cidaris (pictured above) or stumble across the archgriffin's nest while exploring.
After speaking with Hans head over to the quest marker on your map and investigate the blood stain and the body. To the north a little bit you'll find an arm ontop of a rock and spots of blood on the rock that lead to the east, follow them in that direction towards Aeramas' Abandoned Manor. The Archgriffin's nest is just north of it and depending on the time of day determines how things go down.
If it's night time the archgriffin will be on the prowl and will attack you when you get close enough to its area. During the day you'll discover the birds nest and find the Mercenary Contract, the original notice for taking out this griffin (and Geralt learns they offered the other guy more). Looting this will give you a different option at the end of the quest - see more later.
The screen shot above will show you where the archgriffin's nest is/where you have to fight him. As aforementioned, if it's night the griffin will attack you - so meditate until 7pm or later to fight it. Once you finish meditating he Griffon will attack you immediately, however he will circle around a few times before landing. You should take this time to prepare.
Opinicus Weaknesses: Grapeshot, Hybrid Oil, Aard
If you found the Mercenary Contract at the archgriffin's nest when you return to Hans and turn in the trophy you'll get an additional dialogue option. Basically confronting him about giving you less than the reward he gave the other guy. Geralt is a pretty big dick about it but it's up to you if you wanna go this route.
During the Hearts of Stone expansion one of the main quests, Open Sesame: The Safecracker will involve Hans. If you choose the #1 option in the screen shot above, involving confronting Hans, when you return to him for the Hearts of Stone quest he'll be livid with you.
I'd recommend you still choose this option though, as you'll earn more EXP during the Hearts of Stone quest later in the game if you do.