Here's another technique that you might want to experiment with. Elements 8 doesn't have layer masks (other than for adjustment layers), but there is a way to approximate the effect. This gives you the ability to "undo" your deletions and so is more forgiving and adjustable.
Double click your image to convert the background layer to a regular layer. Hold down Ctrl and click the New Layer icon to make a new layer below the image. Do this again to make a second new layer. Sample the blue sky with the Eyedropper and fill the bottom layer with blue, then reset the foreground/background to black/white (press the "D" key).
Click on the top (image) layer in the Layers Palette and then make a selection of the eagle as discussed previously. Leaving the selection in place, click on the middle (transparent) layer and fill the selection on that layer with black by pressing Alt-Backspace. Press Ctrl-D to unselect everything.
Now, again select the top layer in the Layers Palette and press Ctrl-G to group it with the middle layer. You won't see any apparent change, but you have just created a layer mask in effect. To see what has happened, hide the bottom (blue) layer by clicking the "eye" icon. Turn the bottom layer back to visible to proceed with the edit.
Now you need two tools: your brush set to black and the eraser. You can vary the strength of their effect by changing the size and opacity.
Next, very important, make sure the middle (mask) layer is selected in the Layers Palette. As you work on the image you will appear to be moving your tools on the top image, but will actually be working on the mask layer below it. Paint with black and more of the top image will become visible; erase any of the black and the corresponding portion of the top image will be hidden. Lower the opacity of your tool and you will achieve a blending of the top and bottom layers.
Hope I got everything in there. Good luck with your edit!