Artex bubbling repair
First, you must address the cause of the separation/bubbling or it will happen again after you repair. Damage like this is typically caused by moisture, which could be caused by a leak, improper ventilation, insulation gap or improper moisture barrier and is likely on the inside of that wall. This doesn't look like a basement concrete wall but moisture is common on these and difficult to resolve, often involving drainage and waterproofing repair from the exterior. Visual inspection of a drywall wall can often miss important clues, you could try a moisture meter or look above (attic) and below (basement) this spot for clues what could be going on inside.
Once the source of the moisture is resolved, patching drywall is fairly straightforward but matching texture is much more difficult. You'll have best results if you're able to determine and duplicate the original application method and practice on a scrap piece of drywall. Ceilings are often textured in similar ways so videos detailing ceiling texture repair may help if you've never done this before.