I think I'd get a sheet of 3/8" drywall. It's somewhat rare, but available. If your patches need to be 3/4" thick, this will do well and will leave you with a slightly larger arch opening than you started with.

Finish removing the old drywall or plaster to the height of the arch, first. You don't want to have to try and blend with something right at eye level.

Install a layer on the inside face of the opening. Install two layers to fill where your old drywall was around the corner. Now cover it with metal corner bead. If there's a joint in the drywall that isn't covered by the bead, tape that joint as you fill along the bead.

I think I'd get a sheet of 3/8" drywall. It's somewhat rare, but available. If your patches need to be 3/4" thick, this will do well and will leave you with a slightly larger arch opening than you started with.

Finish removing the old drywall or plaster to the height of the arch, first. You don't want to have to try and blend with something right at eye level.

Install a layer on the inside face of the opening. Install two layers to fill where your old drywall was around the corner. Now cover it with metal corner bead. If there's a joint in the drywall that isn't covered by the bead, tape that joint as you fill along the bead.

Plan view:

_________ < ---- metal corner bead
| _________________________
| _________________________ <------- one layer of 3/8" drywall
|| | |     /     /     / |
|| | |<------------------------ two layers of 3/8" drywall   
 |_|_|   /     /     /   |<---- wall stud
 |   |___________________|
 |   |
 |   |<------------------------ old drywall/plaster
 |   |