In order to tame you have to let it follow you while you kill creatures. It will then proceed to eat the corpse, the taming bar raises with each bite it takes. Depending on what you kill determines how fast the taming bar rises. Phiomas worked well because it takes several bites. Keep your eye on it so it doesn't fly off and be careful not let it take damage or you will have to start over again.
I think its somewhat like the sinomacrops feed it, it flies off, comes back then feed it again but with meat or fish mostly raw meat. It would be cool if it would incubate eggs when it has babies,u come feed it once in a while, sometimes it asks u for materials to rebuild its nest until the eggs hatch(idk that's just my idea🤐)