Hi,
I missed the motor current information, sorry.
now you I see four of them... do you want all of them connected?
So we talk about 8A...and even more at startup and even more at the pulses?
Confusing: the schematic and the PCB is totally different in wiring and part values. Show the truth only! Otherwise you risk to confuse us and yourself.
****
Issues of your wiring:
* breadboard --> is not suitable for high current and pulsed current
* thin cables
* no bulk capacitor
* current flow (wiring order)
* GND loop
So it´s no surprise that it fails.
*****
Wiring, just one motor:
* disconnect everything except the motor.
* power supply: red and blue directly to the screw terminal of the driver PCB. In parallel install a 1000uF capacitor (short wires) to the screw terminal.
If by hand: install a 1uF ceramics in parallel to the 1000uF capacitor. Best directly soldered on the PCB.
* if not wired a t the motor: you need a fast recovery diode in parallel to the motor as shown in your schematic.
* you don´t need the 10k series resistor as shown in your schematic.
* Arduino: Use three wires from the 3 pin terminal of the driver PCB and wire them to the arduino.
(No other wires, no additional GND, don´t use the breadboard bus) Install a 100uF bulk low ESR capacitor at VCC and GND of the arduino.
Klaus