Really cool intro... but I didn't get far at all because I could not figure out the swinging mechanism. I was literally stuck on this area for five minutes trying various things to be able to get to that second swing point.
You can grapple the second swing point, pretty much from the position you're in on the screenshot. Just face left and fire the grapple. On the swing back, you can release and make the jump onto the top platform. Hope that helps. :)