Well I didn't do it (not all the way) when we were in Edinburgh, but sent DH on up to the top by himself. I think there must be more than one way up, but the main path from the direction we were going looked kinda steepish, and had what looked like a lot of narrow steps...I don't like steps or heights with a steep dropoff to the side, plus there were so many people coming & going - I didn't want to get stuck in a panic attack on the steps somewhere, and then have a crowd of people waiting on me to continue.
I walked up part-way (before the going got rougher so to speak), and then found a place to sit while he went on up the rest of the way.
Maybe someone who lives in Edinburgh or has been up all the way will have better advice, but it didn't look like a path for me, in any case.