How to remove tight screws from wall plug?
I would try these things in this order:

Use an impact driver to loosen the screw. You can either use a full impact screwgun or air impact tool to remove the screw (make sure you apply lots of pressure against it so the driver does not slip out of the screw head). There are also hammer impact tools available that are more used to loosen stuck screws, and then you use a regular screw driver to fully remove. With these, you place it on the screw, and pound on it with a hammer. If you don't have an impact tool (electric or air-powered) available, this would be a good solution as these hammer impact drivers are relatively cheap (can get them for around $10 US).
Use a cutting tool to make a slot for a flat-head screwdriver. These allow you to apply more torque then a Philips head.
Cut the head off the screw altogether or drill it off. This will allow you to remove the bracket at least, but you will have to abandon the screw shank in place and move your bracket slightly if you need to re-install it.

One more thought, since you said you are using plastic wall plugs. If all that's holding the screw right now is the wall plug, you could also try some gentle heat on the screw, before unscrewing or pulling it out. You might be able to heat the plastic enough to where this will work. But it's also possible the end of the screw is stuck in the concrete. Concrete will also be destroyed quickly by too much heat, so you would need to be quite careful with this method.