Place flexible corner bead over the archway's two bottom corners. Secure the flexible corner bead in place with drywall screws using a Phillips-head drill bit. Place one screw every 3 to 4 inches. Sink the screws' heads slightly lower than the drywall's surface to make it easier to cover them with drywall mud.
Use a 6-inch drywall knife to scoop some drywall mud out of its bucket and place it in a mudding tray. Scoop some mud out of the tray with the drywall knife's edge. Place the drywall knife at a 35-degree angle against the wall with the bottom corner lined up with the flexible corner bead's edge.
Press more firmly on the drywall knife's top corner than bottom corner so the mud is thicker over the flexible corner bead then feathers out as it moves up the wall. Scrape the drywall knife over the wall following the arch of the archway. Scoop more mud out and continue applying a 5- to 6-inch-wide layer of drywall mud over the entire flexible corner bead. Keep the mud layer no thicker than 1/8 inch.
Run the mudding knife over the archway's bottom edge. Fill the entire space between the two corner beads with mud. Hold the mudding knife's edge against the flexible corner bead's ridges and use this as a reference for the mud's thickness.
Allow the first coat of mud to fully dry. Use a sanding sponge to smooth the dried mud's surface. Move the sanding sponge in a circular motion over the mud. Use the mudding knife's edge to scrape away any larger lumps or ridges.
Apply a second coat of drywall mud the same way as the previous coat except using a 10-inch knife. Feather the mud out toward the ends so it blends into the surrounding wall. Spread a second coat on the archway's bottom edge to fill in any holes. Allow this layer to dry completely before sanding it smooth with a sanding sponge.
Spread a third layer of drywall mud, using the 10-inch knife, if the second coat is not smooth enough. A finished wall looks smooth with no lumps, ridges or holes.