You must fix this through the plasterboard and into the studding: make sure you can locate the centre of each vertical timber behind the board. (A metal detector will find the nails used to fix the plasterboard.)---
The method depends on how many people you can get to help. If it's just one other, I suggest fixing a horizontal rail for the mirror to sit on first. If the mirror is a metre wide, you can get at least three substantial screws through the rail into the timber. Then, two or three big mirror fixing brackets will hold the top to the wall (again screwed into the studding). Finally you can drive a couple of screws up into the pine frame to stop the bottom moving away from the wall BUT make sure these screws don't go anywhere near the mirror glass. --- If you have the luxury of several people to help, you could use mirror fixings at the bottom as well. This would look more discrete, but does need some intelligent muscle to hold the mirror in place until the screws are driven home.