No to staples, unless you're screwing a piece of trim wood over it for extra security.
Other option is fender washers and screws, you can see a couple on the sides of the window (note that I don't have as many screws in there as I probably should, my entire coop is surrounded by the run which provides some level of security):
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I hope you aren't doing little vent covered gable vents, it looks like you don't have any vents at all right now, so you need large vents, like most of the triangles opened up on both sides, if you live in a hotter environment.