First read the manual here. It describes what to do to to update the BIOS without taking care of the OS running on the NUC.
Go to the hhttps://downloadcenter.intel.com/download center as explained and input the Intel NUC reference in the dedicated field. Once the NUC reference found, select the BIOS upgrade (top of the list in most cases).
There are several files, the right one is a ZIP file that can be put on a USB key and extracted. It should be referenced as iflash BIOS Update. Accept the terms and download it.
Put the file on a FAT32 formatted USB key and extract it.
Reboot your NUC with the USB key plugged in and press F7 to enter the BIOS menu upgrade. Select the USB device and the .bio file on it. The Intel NUC will suddenly reboot and you will see it updating itself. Wait for it to finish and it will boot back to normal again.