First, unless you have US citizenship or a green-card, studying medicine even at the graduate level (as said above you can't at the undergraduate level), you have virtually 0 chance of getting in.
Secondly, for admission into Harvard for your undergraduate generally, you'll need TOP grades - you're talking about literally the best university in the world, so think far in advance of what you would need for the likes of Oxbridge. Harvard (and top US schools in general) have the lowest acceptance rates in the world and from the UK last year, Harvard received over 900 applications and they gave out 3 offers. 1/300 is incredibly slim, so you'll need to stand out (i.e. have excellent EC's, think Olympic/national athlete or having published books etc), straight A* grades are the BARE minimum.
I went through the process last year and was fortunately made an offer (though I choose Yale instead for personal reasons), but it was a process which was far more difficult/stressful than applying to Oxbridge, which felt like a walk in the park almost by comparison.