Let's assume you have access to some pretty crazy tech but that you still have to obey the basic rules of biology. If you build your cyborg so that the only remaining squishy bits are the brain and perhaps a few others like the heart and digestive system (though it is my understanding that everything but the brain should be theoretically optional as long as you have mechanical analogues that can provide nutrients and oxygen to the brain), your tin-man will obviously be physically superior to a normal human. That goes without saying. But can they catch a bullet?
While a sufficiently sturdy machine should be capable of doing this (I think), the brain obviously isn't. Even if we assume you've overclocked your organic brain's processing power with some form of nanotechnology or additional cybernetic enhancement so that it can react in time to dodge a bullet, the g-forces you'll be subjecting it to by moving it out of the way of the bullet's projected flight path (even by a marginal amount) will turn that poor defenseless lump of meat into a skull full of jelly. That's why you don't DODGE the bullet. You catch and/or preferably deflect it, only moving your completely mechanical limbs and sparing your squishy head from having to accelerate to a few thousand gs.
But does that really work? Would simply moving one of the mechanical parts of your body at high speeds to intercept a fast-moving projectile keep your organic body parts safe from the strain you'd otherwise be putting on them, or is this just a drastic oversimplification of the forces acting on this cyborg when they attempt to catch/deflect a bullet without moving their head or neck?