This is the third pic in a little series I made to sum up the fighting styles I associate with each of the main species in MLP (full list: fav.me/dcab8b3)  
I feel like Griffons and Dragons in the show are very similar (greedy, aggressive, and potentially dangerous) so I wanted them to have similar styles and Muay Thai (a very aggressive style with a lot of options) was a good match for MMA (a very aggressive sport with a lot of variety). This wasn’t based on a particular scene in the show but I decided to use Gabby and Ocellus (who doesn’t have an official griffon form to my knowledge so I whipped one up).  
I don’t own these characters just the pic