First eviction in Georgia, need advice.

[William Jones]

I've had a problematic tenant who I inherited when I purchased a investment property in October. In the last few months she became late, but always caught up with rent, in June she missed a payment completely and the check she wrote for the balance  of May bounced. She had a total due of a little over $900. I sent a letter demanding payment, which she paid $550 immediately, after two weeks of not hearing a word and not being able to get in touch, I served a demand for possession letter, and then filed a dispossession.

July's rent is now past due, and I have a court date, but I think I just realized I made a mistake. The dispossession served was for a partial balance of rent, which tonight I'm learning may not work when it goes to court. Should I call and cancel this eviction process and start again including July, since July is a full month not paid? 

Meanwhile, the day I filed the dispo, the tenant called to tell me the AC stopped working, I sent an AC company out, who had to go out multiple times and thought something seemed fishy, the $380 invoice had a note that during one service call a guy (who was not the tenant) climbed through a window to let the AC guy in. After  having it up and running she called back to complain that it wasn't working again, on the second call he noticed what appeared to be a hole from a screw driver punched in the outside unit through the coil.

This is my first eviction here, was in NJ previously and used to their laws.