Software calibration won't cut it.
You need a hardware calibrator – a colorimeter like a Datacolor Spyder or X-Rite i1Display – to get real accuracy. The built-in Display Calibrator Assistant in macOS is a guessing game that only adjusts white point and gamma curves in software, not the display’s actual hardware LUT. MacBook Airs don’t have hardware calibration tables, so software-only tweaks are limited by the panel’s native behaviour.
Even with a hardware calibrator, the glossy screen and typical contrast ratio of a MacBook Air aren’t ideal for serious photo editing. You’ll get a decent baseline, but don’t expect reference-grade color.
If you’re editing for print or client work, invest in a proper external monitor with hardware calibration support. The Air can drive it fine.