I'd like to use this sort of a half tone effect on shadows shown in this image. How is this achieved?
It looks like it was created with a brush preset or pattern brush.
I would download any preset you find that you like and then just play around with the opacity settings.
It is comprised of several layers at <50% opacity.
This is just a quick example of how to achieve it.
If you want to do this is Illustrator you can find a lot of pre-made vector patterns or brushes. Then you again would just play around with the opacity to achieve the desired effect.