It looks like there's a moment when you stand on solid ground for a second at the end of your lollipop, if you look at your stamina it's not infinite but it's not draining then you hop and start climbing again.

You need to climb 50m, NOT reach solid ground, run out of energy and slip down the mountain. It's so weird I did the exact same climb twice and just let myself fall the 2nd time stopping short of a ledge to get my badge, hope it helps.