How can I hang a heavy mirrored bathroom cabinet?
That sure is a heavy cabinet.  I think you will be fine if you use at least a 2 or 2 1/2 inch #10 or larger pan head screw with a washer. Four screws/washers should be fine if you can only hit two studs, obviously, six screws/washers, two each in three studs would be better. Not sure of the metric conversion, but a #10 is about 5mm. I would not use anything smaller.