@musashidan OP said this was for a highpoly, tho. @JordanLeigh It's not so much about the amount of sides to the cylinder, it's that you didn't plan around the amount of geometry you went with. You could do something similar using other methods, as mentioned before.
Well its not really the amount of side edges that is causing a problem with your initial pic. As has been said it looks like you selected all edges and hit bevel. The trick is to insert edgeloops next to the edges you want sharpened. The closer you set an aegeloop to an edge the sharper it will be. Up to a point. For ease…