How to drill a hole for fixing curtain metal bracket. The drill bit is not able to pierce the metal plate which is about 3/4" under the wall surface.

Can't quite picture what type of curtain bracket you have that has a metal plate 3/4 inch below wall surface. First-- are you sure that the metal plate is part of the curtain bracket and the plate is not actually there to protect an electrical wire?
If you are certain that you should drill through it, maybe you have a dull bit. There is a wold of difference between a sharp bit and a dull bit. Have you centerpunched the metal to keep the bit in place, and are you using a small bit to start? I have never seen a curtain hanger like you have described but maybe I have something to learn.

If you mean that you hit something metal underneath the drywall while trying to mount a curtain bracket, I would say that it is unlikely that what you hit is a metal bracket. It is more likely a screw or a nail. Move over a small distance and try another spot.
Of course that is assuming that this is next to a window.
If where you are drilling is somewhere else and there really is a metal bracket there, don't drill there. Any metal bracket underneath the drywall would be there to protect something, like a pipe or a wire.

If you insist on drilling there however, you must use a metal cutting bit, not a wood bit.

Could be a steel lintel is this is a masonry house. In any event, use a titanium nitride coated bit and turn slowly.