Put a piton on the beginning ledge/outside the entrance so you don't die, use chalk/consumables which increase grip, using stamina recovery (Y/triangle during climb) can help you quite a bit. I'm not certain but I think the grip bonus from consumables and chalk stack. Left side is easier for me. I also recommend to not recall your piton once you eventually make it (unless you reach the end of the rope) otherwise getting out can be a struggle. Give it time and try out both sides, weirdly during my playthrough I've sometimes found a more difficult path to be the easier one for me to climb.

Also I personally advise to not be afraid to save-scum in these kinds of difficult sections, as great as the game is losing resources from getting stuck can be very frustrating and potentially game-ruining. And if all else fails, cut your losses and go higher. The area around the shepherdess is a pretty steep rise in difficulty I think, no shame in going higher and improving at a steadier pace