This seems not to be the method on how speedrunners do it now but for me as new speedrunner I feel this way it's more consistent. The skip involves jumping on the right fire pillar next to main gate after Carpe Retractum Challenge and than jumping over the barrier that restricts you from proceeding outside and doing Care of Magical Creatures. In this tutroial I do this skip from a different angle. It may be a bit slower but it feels more acurate (for me at least). Video Link:

P.S. Sorry for the quality ofmy mic. It's just a cheap 20$ Logitech one.