Step 1: Increase the size of the feet especially towards the CoG as much as fashionable (if aesthetics are not an issue, use U-shapes with openings facing each other and you did it). Have the feet somewhat flexible as needed helps with difficult terrain.
Step 2: Increase the mass of the feet relative to the mass of the head as much as possible. Ideally, the head is lighter than the atmosphere and keeps itself up and the feet each are heavier than anything else combined.
Step 3: Optimize the legs' movement. For a smooth and balanced gait, consider a female-like gait where the feet stay very close to the center at all time and the "hips" provide counter-movement. If you manage to give the Mech enough push with the hind leg to move the CoG well into the front leg's area of stability and move the hind leg over the front leg, you are about as stable as it gets with two legs and minimal joints. The legs would need to be pointed inwards while being placed as far out as possible.
Step 4: Admit that bipeds were a bad idea in the first place and just not worth it if you are not restricted by the number of limbs. We are about the only bipeds out there and even that only because we needed those limbs for utility. [Edit: Same goes for the few other bipedal animals that are not extinct yet. Birds use their front limbs for flying, a much more versatile way of movement, bats even use their front limbs for walking, grabbing and flying.] Evolution does not grow wheels or two additional pairs of legs but Mechs can be designed in any desirable way. I imagine the mad scientist mastering his invention at the end of the story with dozens of joints, counterweights, and such - just in time to get bested by an "inferior" engineer who just builds a tank on tracks.
