find the position of the wooden studs in the wall that the plasterboard is nailed to, and get at least one screw in a stud. If necessary you can run a batten behind the mirror fixed to one or more studs
Often you can detect the stud position by looking or feeling for tiny dimples or spots showing through the decoration, or tapping with your knuckles. Otherwise, drill a hole through the wall where you think a screw should go, and feel through it with my Special Tool (£50 plus p&p). If no stud there, form the Special Tool into a shallow curve and push it through the hole so that it travels sideways, first to one side, then the other. When it meets a stud, mark the distance, withdraw the Special Tool and mark the wall at the same distance so you know where to drill.