Thanks for the feedbacks! I've made some progress on the animation, not yet finished but pretty close.
I included a subtle anticipatory motion, I can't really overdo it, it has to happen fast in-game, and be fluid. The hair are my favorite part, I exaggerated the motion to give the character more energy. Animation is a bit longer than the previous wip version, but still compatible with what actually happens with the game object. For those interested, I separated the hitbox of the object when climbing and the animated sprite, which is displayed at fixed coordinates during the climbing. It's clean, always in the grid, and I just have to make sure that the hitbox is where I display the sprite.
Any feedback welcome!
Just finished this animation, this is visual feedback for the players, letting them know they can also jump directly on the opposite direction when holding on to a ledge. It's not a mandatory step to perform the jump, as I said, only visual indication. The end is a bit hard with the braid, I might rework it a bit, but I don't want to add several more frames.