cut the plasterboard out behind where the brackets are, so cut out 2 bits with a padsaw, say 250 long (300mm rad) by 100mm wide. now cut 2 bits of 18mm ply, 250mm long by 200mm wide. Slide the ply into the hole in the wall at an angle (be careful not to drop it inside the wall, you need to put a screw in the middle of the ply with the head sticking out to give yourself something to hold onto)
Now the ply is behind the wall, centre it up in the hole so it overlaps each side evenly 50mm then screw though the edges (25mm in) of the left and right side of the plasterboard and into the ply which will pinch it all together. Now replace the PB you cut out earlier and screw it into the ply.