Blinking way can be difficult.
What I always do is you jump up with the sword from the unbuilt bridge. You then start swinging following the bridge path. Once you are about to the other end (you will be below the edge) you start swinging to the right. There is a little perch you land on that is next to the wall. Then you jump up and around to another rock that's a little higher up. Then you finally jump up onto the other side.
Takes some practice but after a few tries it becomes way more consistent than the blink way.
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blinking (not the way he showed in the video, other methods are better) is much quicker and more consistent than either of the jump up methods (right or left).