This is a solo INSANE guide but a partner will always help as long as he's not a liability. Obviously this works for any difficulty.
There are two stages in this boss fight. Destroy the Brumak's arm guns and then shoot his legs to momentarily expose the driver to fire. Sounds easy but in reality this is extremely luck based, and all depends how much Dom or your partner die. I pick Dom up almost right away since he distracts the Brumak allowing you to destroy the guns.
Always be ready for the random missile barrage, simply jumping sideways will help you avoid them. It should take half a clip to kill the driver as you bring down the Brumak but the most important thing..always start firing at the Brumak's legs with a FULL clip so you don't get caught reloading when you have those few seconds to shoot the driver.
Here's a clip of me popping this achievement.