I found it’s quite difficult to actually climb onto her back especially if she’s walking in a forest area with few places where you can jump from. The easiest way I have found to get onto her back is grapple onto her throat or belly, while she’s walking just follow around feeding her crystals or primal crystals if you have, but pretty soon she will fly up. At that point if you haven’t been able to jump onto her, the grapple will keep you in her proximity, however it’s very unsafe to stay this way cuz you will take fall damage when she flies up and down and you don’t quite land on her. At that point you want to keep trying to land on her back while keep feeding her. After a few attempts you should succeed. When you’re on her back the only time when she can knock you off is when she flies against a cliff, which due to the smart game AI, doesn’t happen very often. In that situation the grapple hook will also save you from dying of fall.

Grapple doesn’t aggro these things but if you accidentally punch her after you grappled… yea they will likely kill you if you don’t have a strong tame next to you