I usually attach a mask by the ribbons or strings that would hold it on one's head. Is that what those curled things are, coming out of the sides of the mask? If so, and if they are sturdy enough, I would use a 1/4" wide Mylar strap on each side, preferably tucked away under the edge of the mask.
If there are no protrusions sturdy enough to provide the needed support, then you may be forced to stitch through the mask at two or more strategic attachment points.