Well, without knowing exactly how you made it...
The first thing you need to do is create the blue crescent as a standalone object.
To do this, make a copy of the green ellipse and the blue ellipse and put them on a separate layer. Make sure the green one is on top of the blue one, select both, open your Pathfinder palette and click the 'subtract from shape area' button (second one along) whilst holding down the alt key.
This will leave you with a standalone blue crescent.
Copy this new shape and put it on a layer of its own above the other one.
Now move your white blurred ellipse (if that's what it is) onto the same layer as your uppermost blue crescent that you just created.
Within that layer, move the new blue crescent above the blurred ellipse (select it and go Object>Arrange>Bring to Front). Select the whole layer in the layers pallette, click the fly-out menu on that pallette and choose "Make Clipping Mask".
Now make sure both layers are visible, i.e. the layer with the clipping mask that you just created and the one underneath with the solid blue crescent.
Now the easy bit. Assuming you have a white ellipse on top of a green ellipse, simply select both, open your Pathfinder palette and click the 'subtract from shape area' button whilst holding down the alt key.
Essentially you should have three layers now, the top layer with the green swish, the next layer down which has the white blurred ellipse which is clipped by a copy of the blue swish, and the bottom layer which is your solid blue swish.
Create a new layer underneath all the other layers, place your image on it and you should get the effect you want.
