Contract: The Griffin From the Highlands - Velen
Location: Crow's Perch
Quest Giver: Crow's Perch Notice Board
Other Requirements: Complete most of the Master Armorers Quest to unlock this one
This quest will become available during the Master Armorers quest which you get from the blacksmith at Crow's Perch in Velen. When you complete about half of this quest the female smith will ask you to bring her back acid from the archgriffin and Geralt will remark about a contract on the beast, when you see that scene this quest becomes available.
First thing you'll need to do for this quest is travel to the north of Crow's Perch and to the first quest circle. There is a hand to find here as well as some Archgriffin foot prints which lead north - but you aren't actually required to find this. Just head straight north of where this quest circle is and you'll find the Archgriffin's nest.
If you're having trouble locating this area, use my screen shot below for further guidance. Or, use your own map and go to the area with the Guarded Treasure on your map, or if it's still a ? it is the only hidden location in the entire area. You'll stumble into the griffin if you come to this location, guaranteed.
The battle with the Archgriffin is a piece of cake, use your Crossbow or Aard to bring him down - or just wait for him to land occasionally and whack him with your Silver Sword. After the fight if you decide to go on a treasure hunt, don't bother. I spent some time looking around for the alleged Guarded Treasure but came up short, I found a google search where someone had similar results. I assume maybe the treasure appears later in the game.