The cheapest shotgun requires 3 upgrades (at $400 each) to max out its damage. You should have no problem obtaining this shotgun through game play (although you can always buy it if necessary). Once you have $1200, save the game, go into your inventory, choose the shotgun, view it's info, then upgrade the damage three times to unlock the achievement.
You can then reload the game to get your money back, assuming you're not actually trying to use the shotgun as an upgraded weapon.