You will need two applications, the Arduino IDE and the Hex Uploader below.
Download and unzip the Arduino IDE from HERE. Note it MUST be placed in your Applications folder when extracted.
Download the 'Hex Uploader" application from HERE. Once downloaded, extract the contents to your Desktop. The result will be an application called 'Hex Uploader.app'.
Ensure you only have the hardware device you intend to update connected via USB.
Start 'Hex Uploader' by double-clicking on it
In the first section under "Arduino Type," choose Mega - ATmega 2560
In the Serial Port port, ensure you have selected the COM port applicable to the hardware being updated (typically usbmodemxxxx)
In the Baud rate, ensure it is set to 115200.
Once configured, simply hit the "Upload a Hex File" button, which will prompt you to select the .hex file downloaded above. As soon as you choose that file, the upload will begin. The upload will only take a few seconds and, when finished, will read, "avrdude done. Thank you".
Disconnect and reconnect the USB cable.