Howdy,
This is one of those things that can be easy or hard, depending on the situation.
If the screw just broke and isn't seized (which is most likely), then you can just use a drill bit that's a smaller diameter than the screw (so like a 1/16" should be fine) and drill in the center of the screw. There's a really good chance that just the friction from drilling the screw will wind the broken bit of the screw out, without you drilling all the way through the screw itself. Try pretty hard to drill in the center of the broken off bit of screw btw. Ideally you'd use a center punch to punch a divot in the center to help keep the drill where you want it to be.
From there, it gets harder. 🙂 If the screw is actually seized in there and just the friction from drilling doesn't get it out, your best bet is to drill it with a #29 drill (which is the tap drill for an 8/32 thread). You have to be pretty close to the center of the broken off bolt for this though, since you'll wipe out the threads if you're off center or not drilling parallel to the hole/screw. If you can drill it, then chances are that you can use a pick or an 8/32 tap or maybe even another screw to clean the remaining metal out of the threads.
But if you're doing that, chances are that you're going to end up wiping out the threads in the plastic tendon guard... If that happens, you could just use a longer version of that 8/32 flathead screw and use a locknut on the back of your skate. It would end up sticking out of course. Or maybe you could tap the tendon guard to the next size up from the hole you had to drill.
In all of the situations where the bit of screw doesn't come out just from the friction of drilling, the easier fix is to just replace the tendon guard.
Note that in my case, the screw came out with the friction from drilling. The rest of what I wrote up there is just educated guesses from "I've had to deal with broken off screws / bolts before".
Good luck!
Mark