The phrase "monkey off one's back" means to finally get rid of a difficult or burdensome problem or task that has been causing stress or trouble. Full definition
So how long will it take to get that debt monkey off your back, and how much does it matter? (moneychimp.com)
The practice of being in the moment with your breathing will begin to train your brain to focus solely on the task at hand and get the stress monkey off your back. (entrepreneur.com)
Get the 1 and done monkey off our back OR have a legit chance to win it all? (sbnation.com)