There is technically no such thing as a partial bankruptcy. If you file for bankruptcy, you must include all of the debts that you currently have. Some use the term "partial bankruptcy" to denote chapter 13 bankruptcy.
Chapter 13 Bankruptcy
Chapter 13 bankruptcy denotes the type of bankruptcy in which you set up a payment plan with the court that allows you to pay back all or part of your debt over a given period of time.
Chapter 13 bankruptcy is the preferred type of bankruptcy, because your credit score is not damaged as much and is easier to repair after a shorter period of time when compared with chapter 7 bankruptcies.
Partial bankruptcy will allow you to keep all of your assets as long as you keep up with the payment plan set up by the court.
The payment plan set up by the court will take into consideration how much money you owe, along with how much money you make, and set a minimum payment that must be made each month.
Though it is considered the preferred type of bankruptcy, partial bankruptcy should still be seen as a last option in your attempts to pay off your debts.