For Molycorp: seek to become nationalized either de jure or de facto (by lobbying for massive subsidies or import tariffs). A private enterprise will have a very difficult time against a nation state with effectively unlimited cash and manpower.

For the SmallCo vs Amazon example: either superior branding&marketing or protection via patents. If you try to differentiate through pricing, Amazon can sell at a loss for too long for you to survive.

But tbh in either case it is like a third world dictator asking "how can I win" when the US is already invading. You can't, the best option now is to cut losses and retreat so you at least stay alive.