Looks like you have damaged the outside metal corner.
To fix this right and make it look all the same just uses some simple tools, it's just going to be a royal pain, many step job but any home DIY can do it.
You will need a hammer, hack saw, new corner bead, 6" wide drywall knife, a Qt. of all Purpose drywall compound, primer and paint, paint brush, tin snips drywall or or roofing nails, medium sanding sponge.
I would tap the area with a hammer holding it flat to the the metal corner 6" above and below the damaged area to break up the drywall compound, then you want to use a hack saw to make a shallow cut to make minimum damage to the wall.
Remove the metal corner piece.
Cut and apply new outside corner.
Clean up the area making sure not you leave any loose drywall compound or paper,
Apply drywall compound in thin layers.
Apply one coat and let it dry over night, it's likely going to take three coats to blend it all in.
If it's done right you only need to sand the last coat.
After sanding use a damp cloth to remove all the sanding dust.
Prime then paint.
DO NOT TRY AND USED THE PRIMER AND ONE PAINT!