This Dino is commonly found in the snow biom or sometimes near the red obelisk, the dino itself is really slow but it unables you to pick up large dinos, you have a platform saddle and to tame a quetzal you need meat or rex kibble but you need prime meat jerky which you can make in a preservation bin by putting some oil and cooked prime meat and to start the bin put in some spark powder which is made in mortar and pastle. You’ll need some tranq arrows like 20-40 or tranq darts but there is a high chance that you’ll kill it with tranq darts so use tranq arrows or toxicant arrows, you’ll really have to look for a quetzal cause they aren’t, well I won’t say not common but you don’t find one so easily.
There is usually at least one quetz roaming around the red obelisk and craggs Island. Go over there and kill any and all quetzals that aren't of your liking, and then fly to above the nearby swamp or The end of the red lake (or further). Then fly back and be sure to check above the beach area between craggs and the obelisk which is separated to craggs by a thin water path. If no quetzal has spawned there then look around and west of the obelisk. If no quetzal has been found in either area then try flying further away or waiting 10 sec before going back. This method works especially well on evolution event which is when I've mostly tried it. Good luck!