Lynels... are different in different games. In some games, they have the lower body of a lion or tiger, a human torso, then the head of a lion/tiger... but in the original game, the first Legend of Zelda, they were almost staight-up centaurs. They had the horse body, human torso and lion heads. It was hard to tell just what they were in the actual game, but their official manual art has captivated me ever since before a lot of you were born. I have been awaiting a return of classic Lynels to the games (particularly a 3D version envisioning of the monsters) and have been... sad.
I'm keeping my vote for gryphons, but I've been trying to think of mythological creatures that haven't been mentioned that would be a good addition...
I could see banshees as a more dangerous version of poes. I could see a screaming banshee as a boss, something you have to fight around to fight, lest Link be stricken by the soundwaves.
I could see a fight with a pair of or a group of harpies as being something like the Twinrova fight. Think about it... circling harpies that swoop down, trying to part poor Link from his liver...
Manticore! I can't believe I'd forgotten this beastie. One of them plays a sort-of-villain in a novel I wrote (where one of the two main characters is a gryphon...). A manticore is a beast with a lion's body, a man's face, three rows of razor-teeth set in a shark-jaw-of-doom and a big scoripion's tail. In some of the lore, they could shoot poison barbs from the end of the tail. They are voracious man-eaters. This could be a creature that not only bears its teeth and leaps agiliy like a lion, it could present a posion-risk for Link, shoud Nintendo wish to introduce poisoning as a hazard (like what is present in Pokemon). This could be the perfect application for a world that also has gryphons because Link's collection of a "gryphon's claw" (or a bunch of them) can allow a poiton maker to make an antidote, which he will need for the later boss battle with the manticore-based monster.