I'm not sure if what I'm about to say would fulfill your needs, but there's a workaround I've successfully tested:

1. Select all messages with attachments you need to save, that is, to extract its attachments at once;
2. Forward them as a MIME digest to a local address. My choice is forwarding it to a noticeboard address;
3. Open the forwarded MIME digest in the noticeboard and select the Attachments tab. You'll be able to see all attachments of all those selected messages in the classical tree view you already know;
4. Select the attachments you want to save and click the Save button;
5. Select the "Prompt for a filename for the first attachment, etc..." radio button, then "OK", and they'll be sent to the target directory;
6. Finally, delete the noticeboard entry when it is done to save space.

I wish to select multiple messages that contain attachments and export those attachments to files stored on my disk.  How does one do this within Pegasus Mail?  Am I missing something here?  Thank you.

I don't think you're missing anything.  There isn't a way to select multiple messages and save their attachments.  Message attachments can only be worked with from within the Attachment tab of the message reader window.  Multiple attachments to a singe message can be saved simultaneously.

That's what I figured.  I ended up saving the messages to a file and using munpack on each file to extract the attachment.  Too bad there isn't a native way to accomplish this.