When you have tamed your 1st Quetzal... Contrats btw ! ...Build a thatch box using wooden doorframes on the Platform saddle.

To tame a 2nd one, simply charge the Quetzal you want to tame and when you got him on the box, Dismount your Quetzal. Then, you can KO him in the box and use my "Air Taming" method.. I did IT once and took me 6 hours.