I got PageSpeed 100 (desktop and mobile) using two WP plugins, W3 Total Cache and Autoptimize. I have posted detailed directions here:
http://baruchyoussin.com/configure-w3-total-cache-plugin-settings-for-pagespeed-100-grade-part-1.html
All my posts (including this one) get 100 almost always (depending on server response) while a couple of pages are a little short.