Drywall – Hanging heavy object in bedroom

You'll probably have an easier time using a picture hanger than a screw, and it will leave your wall in better shape when you remove it. Picture hangers transfer the downward force into pressure into the wall because the nail is mounted at an angle. The screw, on the other hand, is being bent because you're acting as a lever, where the stud is the fulcrum, the drywall is just empty space, and the wire is the force applied at the end. Even if you get a stronger screw, you're still placing a significant twisting force into the stud.

You can't use your typical picture hanger for a task like this. The small hangers that come in most kits are rated to only 20-30 lbs. However, you can find hangers like this one that is rated to 100 lbs (and I'd still use two of them, since it will make adjusting for level much easier and reduce the risk of failure).

The other option is called a french cleat which are two interlocking rails, one that attaches to the wall, and the other to what you're hanging. As long as you install them both straight and level, you don't need to adjust the mirror for level, and it distributes the weight across a larger area, reducing the risk of a failure.

By far, the best approach is to attach either clips or a frame to studs (either wood or steel, depending on your construction).

If the panels are being arranged at the same level, you could run rails horizontally along the wall at the base and top of the panels. These could be made from two pieces of molding, one slightly thicker than the thickest glass panel (about 3/8 by 3/4) and another thinner wider piece on the face (about 1/4 by 1 to 1 1/4) creating a lip. These could be screwed into the studs and painted to match the wallboard.

In a concrete wall, the strip could be mounted using masonry anchors every 8 to 12 inches.

An alternative is to mount mirror clips at the top and base.

However panels of this weight really need stud mounting, so the clips would have to align with the studs, and that might be a problem with spacing. In a concrete wall, mirror clips could be used, but again, need to be placed at least 4 per panel in the base.

It is theoretically possible to use mirror clips with other mounting devices, such as toggles, but you would need several in the base of each panel, as well as two at the top, and the weight would make this very iffy.