Trying to remove a single handle shower faucet with stripped out set screw
I assume you want to replace the faucet.

Options:


Drill it out.  You don't care if you wreck the stem of the valve.
Drill and try an extractor.  I usually never can find one the right size.  I have a set.  Somewhere.
Once your pretty sure that it's not holding the handle on, you may need additional persuasion to get the handle off.


Start off with a low viscosity lubricant, such as bolt-out.  Caution may change the colour of grout.  
The handle may be cemented on with calcium/magnesium carbonates (what makes water hard) Soaking in passivated muriatic acid may release it.  This will take hours to days.  Caution:  Review safe acid handling.
If the handle is metal you can try heating it with a heat gun.  If the valve itself is plastic this may make life more difficult.
If you decide to to pry it off, protect the wall with a couple of chunks of 2x4.  Run them horizontally and pry from above and below.  If working alone, you can hold them in place temporarily with duct tape. A 2 foot chunk will span standard stud spacing.  This, I think will minimize any flexing of the wall which might crack tile or grout.
A better way may be to rig something using puller jaws and a a slide hammer.



In response to a comment:  Turn off the water, and have your replacement parts ready.   Depending on how cheap the contractor who built the house was, there may or may not be individual shutoffs for the shower or just hte bathroom.  I've done many repairs that required shutting off water the entire house.  As a result of this, my first step in a repair is to add additional shut off valves.  (I live a 40 minute drive from the nearest big box store.  Few repairs are done without at least two trips to the store.  Being without water all day isn't a win.  I now keep a couple of quarter turn ball valves in 1/2" solder ends (since I have a copper plumbed house) on hand so I can start with that.)