I'd recommend using a Quetzal with a slingshot ,bolo ,and crossbow. First acquire mentioned things and go out and find one. Hover behind peligornis and make sure you're facing land. Shoot Peligornis with the slingshot causing the Peligornis to fly towards land. Once over land bolo the Peligornis dropping it to land then pull out crossbow with tranque arrow and shoot it in the body because there is a multiplier to its head. You are more likely to kill it with a headshot so make sure to avoid that. Once knocked out I'd recommend the starve technique just so you don't lose any Compy Kibble just in case it's killed or attacked making it no longer a perfect tame. If you don't have a Quetz use a Pteradon and just hit it with a regular attack
Ever need lots of raw fish. Easy! Instead of swimming around in the water risking getting attacked by megapiranhas, simply make a saddle for your Pelagornis, Ride it into the water, and it one shots every small fish.