Keep the boss of your boss off the back of your boss. means?

"Keep your boss off your back" means "avoid being criticized by your boss" so your sentence means "Don't do anything that will cause your boss's boss to criticize your boss." A more concise way to say it would be "Keep your boss's boss off your boss's back."

it means do what your boss asks for as quickly and efficiently as you can so your boss looks good when he sees his boss.

I think that's what it means.

means you have to many bosses..