How to burn bootloader to ATmega 2560 using Atmel Studio and AVRISP mkII?
In the Arduino IDE (1.8.7 is the latest I think):
Select Tools, Select the AVR ISP MKii as the bootloader.
Select the correct board type (2560).
Select Burn Bootloader.

Pretty simple, and it sets the fuses for you.
The AVR ISP MKii does not power the board, be sure to the the USB cable to the PC connected for power.