For the hard badge, I found the shotgun and napalm the easiest combination to run with. You get enough rocket soldiers to avoid needing to take a rocket yourself, while the shotgun's spread takes out all the hard to it things in the corners. Only other thing to worry about is avoiding the screen bombing (the three cars come down just before it), I found staying at the bottom left and immediately moving to the middle as soon as the middle bomb landed meant I lost no one from it, making the rest of the run a lot easier (use napalm to kill the cars to let you do this). Also use napalm pretty much every time you can, with the top upgrade it heals your guys when you use it (and is the quickest to come back up).
 "Battalion Commander"){kind=icon}