I found that with many of my clients’ websites the problem is an admin uploading huge photos to the site. No optimization, just loading 3000px by 3000px, 300DPI photo. Teach your clients how to deal with large images.
Note the score before and after your changes so you can document your work. You dont need to fix all of the issues here (impossible) but taking care of even some of them will significantly increase the speed of your site.