Caveat - this assumes that the distinct-for-legal-reasons pseudo-Godzilla evolved using life processes similar to those found on earth. While other building blocks have been speculated upon, no one has a solid idea of what anything beyond single-celled creatures based on (for example) silicon would look like, so speculation on mega-fauna is just shots in the dark.
Taking your points one at a time:
Height of "several hundred feet" - notwithstanding collapsing under its own weight (which it would certainly do outside of water - no bone is strong enough to support even its own weight, let alone supporting muscle), land animals cannot get that tall. The structure would be untenable, blood pressure would have to be astonishingly high... you just can't have anything much taller than the tallest dinosaurs of antiquity. So you're limited to circa 18m.
In addition to this, the only reason anything would evolve to that size would be if there were sufficient prey around to justify the enormous investment. Whales can manage it by grazing - dinosaurs because there were other dinosaurs. The sheer volume of food required by a multi-hundred-foot monster might make it completely untenable in and of itself; it would have to be constantly eating just to stay alive.
Developing an Upright Stance - Allowing for the first impossible bullet point, the reason for this is the same as other bipedal evolutions - speed and reach. All other things being equal, two legs are more maneuverable and faster than four.
- Adaptations to allow for an amphibious lifestyle - amphibians exist. Whole groups of creatures that can stay underwater indefinitely. No conflict here, aside from gas exchange problems (the reason the largest creatures are mammals is because lungs are way more efficient (half again as efficient) as gills. So your giant creature will have trouble getting sufficient oxygen underwater, but if it's mostly sessile, that's potentially addressable.
- Be impervious to conventional weaponry and have the ability to quickly recover from fatal injuries - Armour, scaled up, could resist many ballistic weapons - just look at armadillos. A minor point here, but if it's a fatal injury, recovery is, by definition, impossible. Rapid recovery from grievous injuries is potentially possible (for example, the axolotl), but the energetic cost of healing is proportional to the size of the organism, so it's hard to imagine that your monster could also carry around enough fat (in addition to its impossible mass) to power the process.
- Atomic breath - nope. There is no chemical process that approaches the destructive power of an atomic weapon, and and no potential biological material that would be capable of shaping and resisting the forces involved, even if there were. Assuming that some magical energy source were employed, the only way it could be shaped would be if a good part of the projecting orifice (the mouth, in this case) were ablated in the process.
All of this assumes, as I said, that we're using carbon-based, earth-like life. It's possible that something resembling life but using processes entirely different from what we're familiar with could address some of these issues. Some of the height issues could be addressed by the creature living on a very low-gravity planet. But assuming you want this thing to be able to tap-dance through Tokyo, it's straight-up impossible. There is no conceivable evolutionary path.