To make it work with physics let us think would you would have to do with just box2d. It has similar limits as with C2: circle shapes and polygons, but no recommended limit on the point count. This is just to point out that that library has no concept of other curves so most things need to be approximated by polygons.
Probably the simplest to do in C2 would be to use a sprite with it's origin on the left and a height of 1. You'd take the vector image and break it up into a poly line alone the edges, then create a sprite per each line. The actual drawing of the terrain could probably be done with the canvas object.
The one con would be possible tunneling because we'd have only a thin wall to collide with. You'd probably need to set the physics property "bullet" to on. It could work with other behaviors but having objects get stuck inside the terrain is more likely.
Another option instead of a thin collision edge around the terrain you could take the polyline edge around each shape and triangulate it, then take those triangles and split them into right triangles and create a bunch of right triangles. This would give a more solid feel to the shapes, but the object count would be much higher. Not to mention getting a good trianglulator working would take a bit of time.
To do either in an automated way you'd need to make a vector image file format reader or somehow export just the polygon lists for easy reading.
Here's a physics test of the first idea:
https://www.dropbox.com/s/8mq9enadn2xvq ... .capx?dl=1
I made the curve in inkscape and exported as a plt file since that seemed to be the simplest to parse.
seems to work ok.
Here's further testing. The image from inkscape was also exported and used as an image.
https://www.dropbox.com/s/5yhh6eycbxxck ... .capx?dl=1