Once you get this tamed, make a shit ton of tranq darts, a lot of meat, and bio-toxins; then go to the Ice reigion and find a Giga. Fly over it and start shooting your tranq darts at it and it will eventually be uncounsious.
These guys seem to be like a glass cannon. Able to hit hard and not take much damage unless it a really high level. Also low stam. Be careful of that even though they are fast. Also get a low level female and male and have them breed to make egg for griffin kibble. This will be used for the high level one.