Hang heavy mirror cavity wall

[samk]

Hello All,
I'm seeking advice on how best to hang a heavy mirror (best guess about 10-12kg) on a wall that has 10mm plasterboard. The wall area is about 3ft wide and the mirror is about 1.5ft wide with the holes for the screws (4x) on either long edge. I've identified the joist but this runs down the middle of the wall.
Should I use toggle bolts to attach mirror to the 'cavity' part of the wall but also drill holes into thewooden mirror frame and use anchor bolts to attach to joists/?
I have very limited access to the part of the cavity. Should I reinforce the inside of the wall where the toggle bolts go through on with either metal or wooden slats (straight or round) to help spread the weight? I've attached a simple drawing to help illustrate. Please advise.
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[joe-90]

As long as you go into a solid part of the wall frame it doesn't really matter what you do. It only has to take the 'sheer' forces which aren't great.

 

[samk]

Quick update: I managed to securely hang the wall mirror (12kg) on the wall using 4 toggle bolts. I did reinforce with a pair of 9cm sq metal plates to help distribute the weight. So far it's holding up very well.
Thank you for the advice and tips.
Onto the next project