Problem Exporting a PDF

Are you sending a PDF copy of the document to a company to get certain kinds of print work done? If so, it would probably be best to talk to them on the phone about specific document settings and PDF export settings, particularly if they expect to simply be able to drop the file into a print queue and output it. Depending on the situation you may have to export each artboard as a separate PDF file.

I would also use a strong bit of caution if ramping up compression levels or down-rezzing resolution of images to reduce file size. Those changes will affect print quality. The quality hit can be really visible in large format printed output. If the PDF file(s) can be saved without the Preserve Illustrator Editing Capability setting checked that will reduce the file size quite a bit.

​@Friendly_grace4b88 when you save your PDF, you can save as a PDF with the artboards selected:
 

Select the smallest file size preset
 

And you can also change the compression even further, but, your images quality will also go down too​​​​​​​

Also, if you open the file in Acrobat, you can even reduce the PDF further. 
 

Just how large are the images?

Have you considered optimizing the images in Photohop before placing them in Illustrator? If you have a huge image and then scale it down to the size of a stamp and then maybe apply a clipping mask and add some effects over it, Illustrator will have a pretty hard time exporting that.

Also: which PDF settings? 

​@Friendly_grace4b88 What settings do you use when saving as PDF? By default Illustrator saves the .ai file with PDF compatibility, so it already saves a PDF. Did you turn that option off?