Speed optimization is done via hand-coding internal server/website files. Caching plugins have a limit to what they can do (usually fail to exploit the maximum speed potential) and generate issues.

Most of the time I see issues having to do with slow server configuration and website misconfiguration, redundant plugins that slow down performance, non-optimized images, CSS, JS, etc.

I fix all errors originating in server/website and optimize TTFB, CSS/JS minification, reducing external calls, adding expires headers, images, etc.