To unlock this achievement on Xbox, start a flight in the Airbus A320neo but make sure to use the default livery as changing this stopped the achievement popping for me.
Now choose an airport and select a parking gate to depart from. Select an arrival airport if you wish and click to start to fly. Once loaded in, the plane will be parked with no engines running. Just hit RB + Right Dpad to start the engines and the achievement should pop immediately