OK, still need answers for some the questions I asked (but only about the load you actually want to drive).
But in general:
R8, 9, and 10 should be reduced to 0.07 ohms 5W or therabouts. These may be hard to get, so you might be able to parallel up 9 0.22 ohm 2W resistors.
The heatsink should be larger or perhaps forced air cooled.
The traces on the board carrying the current should have wires capable of carrying the current soldered along them.
D4 should be upgraded to a something with a higher current carrying capacity. There are a number of high current diodes in TO-220 packages (with 2 leads) that may be an almost droop-in replacement.
The BUK9535-55 is probably OK for 20A
R1 is the biggest problem. Turning the mosfet off this way is slow and will contribute most to the dissipation of the device.
Changing the circuit to use something that will actively pull it low would be better.