Hanging bathroom mirror to tile?

If it has mounting brackets on the back, I would use a proper drill bit. Get some plastic anchors, and secure it either into the grout lines or straight into the tile. You would have to be very careful as to not break your tile, but it is possible if set drill at a slower setting, not applying too much pressure, eventually it will go through .You will need a bit that drills into mortar, etc. From there, attach proper screws. I would recommend using some liquid nails, just to give it added stability. Place enough liquid on the back of the mirror, and secure using mounting brackets, from there push down on the mirror, allow to dry.