Once you have a Polish Apple ID, just sign into this account on your iPhone, then you'll automatically be transferred to the Poland App Store, where Battle Bombers Arena is officially available. To do this, simply create a new Apple ID using a realistic home address from the country where the game has been released - in this case, Poland. Besides that, the App Store's region restrictions will also need to be bypassed before you can download the game in the US.
To play Battle Bombers Arena, your iPad, iPhone, or iPod touch will need to be running iOS 7 or higher.