I propose to measure the amount of time that user spent in each section. It should be at least 3 seconds to get the badge.
There's no real sure-fire way of making sure somewhere reads all of it. You can add in complicated things, like making users click-to-expand every section of the FAQ, but that still doesn't really guarantee anything. All it guarantees is they know how to click their mouse.
If people really don't want to read it, they're not going to read it. All the badge really does is get the user to the page so they know about it, and encourage them to look it over.