Looks like the bracket was attached to the molding (?) with a screw that was too short.
Remove the bracket carefully. You need to salvage the piece of the trim that the screw pulled out - the part behind the bracket. Glue the trim back onto the molding, then patch with some wood filler, sand, and paint.
Reattach the bracket using a longer screw that goes through the wood trim, drywall (or plaster), and into the 2x4 that should be below the window itself. Pre-drill the hole so that you don't split the trim.
Remove the bracket so that you can work. Make use of the hole in the wall board to poke around in the wall to locate the nearest wall stud. Patch the hole in the wall board with some spackling paste (preferably color coordinated to the wall). Replace the bracket, lining it up with the stud. The screws placed in the wall need to be long enough to penetrate the stud at least an inch or so.
I'm not thinking the renter should be held accountable for the failure of this poorly installed bracket. But I'd need to see the other brackets and know some details about the failure, i.e., if the renter stood on the shelf then he/she should fix it.