Deepest Sword

I got it through trial and error, which makes sense given the reference. After the checkpoint in the cave, you may use the lower or the upper path. To get to the upper path, you must try and use your sword to pivot just after the checkpoint, trying to spin it so the sword will anchor on the ledge and pull you up.

I don't think the achievement unlocks if you start directly at length 2, I recommend starting from scratch just to be sure.