First , if it feel to tight or slip usually you have the wrong size screw driver.
Second At this point the smart way would be to remove the board cover the area arround the shield and use a dremel to cut 2 slot in the screw. This way you will be able to use a larger Philips to remove it.
You might also consider a "screw extractor" tool... they're designed for exactly this type of situation.
I guess you mean one of these devices your hit with a hammer and then convert that force into a turning motion? Those are quite destructive and I won't dare to use these on a PCB.
You need this