Will happen with the natural achievement progress as this is the furthest you need to go to get the 1,000.
The end of a Zone is signified by a red portal that you will walk through.
You will naturally do enough damage to reach Zone 10 without any real difficulty. You can open chests along the way to unlock new weapons or ways to enhance the weapon, but it isn't needed as you will do enough damage naturally.
You also can't die so leaving a plugged in controller and walking away will get this naturally even if you do nothing but... idle
