I’m glad you asked because hanging a big mirror can be tricky. Although some ordinary picture hooks are rated to carry a 25 lbs. load, I wouldn’t trust them for your job. These hooks use a single finishing nail penetrating the drywall at an angle, and I wouldn’t rely on this to support a large mirror, no matter what the package says. Mirrors are regularly cleaned, adjusted and bumped into, so use something beefier.
If your mirror is just a flat piece of glass with no frame, plastic mirror clips work well. They fasten to the wall with screws driven into plastic anchors set into predrilled holes in the drywall. Two clips placed an inch or so from each corner on each side of the mirror will do.
If your mirror has a frame with a wire on the back, as pictures often do, then I recommend fastening flat metal hooks to the wall with screws driven into threaded plastic anchors. Use two hooks and anchors to make the mirror more stable. I made and installed a large, heavy frame and mirror at my place using this method and it’s worked perfectly over the last 18 months. Just to make sure, I installed two separate wires on the mirror frame, in case one broke.