125A is pretty scary stuff. At 36V, you're looking at a load with a resistance of 36/125 = 0.288 ohms. Is you wiring going to be up to the size necessary to be negligible relative to this this? What are you going to mount the MOSFET on? It ain't going to be a breadboard or a regular PCB.
Your MOSFET has an on-resistance of 4.2 milliohms, quite respectable, but that means it will dissipate 125^2 * 0.0042 = 65W of power at 125A. Nuh-uh. It'll put on a brief light and sound show once, unless (maybe) it's well bolted onto a massive heat sink or air/liquid cooled.
When switching such large currents, too, transients can easily (well...conceivably) couple into the drivers so you have to be really careful using IC's like the HIP4081A and keep it protected.
If you're not perfectly sure of what you're doing here, I'd stay away from anything that requires 125A at 36V: that's a 4500W power driver you're trying to build. Only experts do this. Beginners end up building sources of fire.
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Ruggeduino: compatible with Arduino UNO, 24V operation, all I/O's fused and protected