Set the fills to be an off-color. Something foreign to the rest of the artwork.

[![enter image description here][1]][1]

 1. Select all
 2. **Pathfinder Panel** > `Merge` button
 3. Use the **Direct Selection Tool** (white arrow) and click on of the off-color areas to select it.
 4. Choose `Select > Same > Fill & Stroke` from the menu
 5. Hit the <kbd>Delete</kbd> key.

[![enter image description here][2]][2]

Merge combines areas of similar color, regardless of their stacking order, and removed any underlying elements. So, by Merging you eliminate anything which was underneath the fills. Then remove the fills if they are not to be part of the artwork.


  [1]: https://i.sstatic.net/JsO2q.png
  [2]: https://i.sstatic.net/GnzY8.gif