I do not think that this needs a guide because Stay Down and Devastation achievements already have guides, however, their solutions recommend high level cards and custom maps. But if you are just starting the game and are in a hurry to get this short term (to maintain an achievement streak, etc.) than I suggest playing as gunner in 50 wave horde on beginner.
After wave 3-4 you should have enough power to purchase a tri-shot and level up your ammo regeneration perk to level 4 or 5. I recommend the tri-shot (4,000 power) over the mulcher (3,000 power). Although, the mulcher is cheaper and holds more ammo, the accuracy of the tri-shot makes it much more effective. Focus on upgrading you ammo regeneration perk first then your health perk. It costs 24,250 to fully upgrade each perk.
Perk costs are
To fully upgrade both the ammo perk, health perk, and purchase the tri-shot you will need 52,500 power, which you should have by wave 6-7. By wave 10 you should be close to 100,000 power. You could use that to up grade the ultimate duration perk or the damage perk. However, the duration perk only double the ultimate from 6 second to about 12 seconds and the damage perk may only effect for load-out weapons, not the heavy weapons but I am not sure on that.
In any event, once your health and ammo regeneration are fully upgraded with a heavy weapon you are basically a walking tank. There are only four things to worry about:
1. Shock Grenades (which make you drop your heavy weapon),
2. Sires (which can still capture you from behind),
3. Matriarch (which your heavy can not damage from in front), and
4. Chasing down power while carrying a heavy weapon (focus on protecting your taps).