Collecting old back rent

[James Mc Ree]

I have a tenant who paid only half the $1,200 rent back in September 2019 with a promise to pay the balance in installment payments.  I received 1 small payment in October 2019 and none since.  The tenancy was supported by Section 8 at about 50%, then went to 100% starting in October 2019.  I've given several notifications to the tenant that unpaid rent plus late fees need to be paid.  The tenant responds she intends to pay, but had lost her job and has to pay for food and electric, etc with nothing left over.

I sympathize and at the same time want to be paid.  I've tried the usual approaches, including "pay for the place you live before you pay to light the place you live" with no success.  At this point, I think I need to step up my game.  I am not interested in evicting her since Section 8 is paying 100% of her rent monthly, but not her liability from September 2019.

What is my best option?  I am thinking my next step is probably to threaten then execute suing for the money owed ($571 rent + late fees = $1,000+).  Does obtaining a judgement help me in any meaningful way?