Oh and I used to have two awful neighbours like this when I bought my first flat in my late twenties. Both were in their fifties, alone and not very friendly. They complained about everything, always trivial - the noise of my hoover, the delivery of new flat-packed kitchen units for my new kitchen, the smell of new paint, and then a mysterious set of leaks which both of them claimed must be coming from my middle floor flat.
At first I was sympathetic, but the upstairs neighbour sent me a letter one day accusing me of all sorts of strange things, including the memorable lines that "you now live in a private block of flats in the west end. Please behave accordingly" and "You think you can come and go as you please". The downstairs neighbour used to leave all her shoes outside her door in the communal hallway, it did look messy and so following another complaint about me using my hoover, I marched down and knocked on the door and basically shouted at her for 10 minutes, telling her why she was an awful neighbour.
The following week, there was an odd incident involving the upstairs flat - the upstairs neighbour had moved out of the flat 6 months earlier and rented it out as an AirB&B. I took some stuff out to my bin in the garden about 9.30pm and received a complaint about this the next day - goodness knows what that was all about but it was rented to a single male and I wasn't happy being spied upon.
The next day the tenant went out, leaving the bath running and flooded the entire block of flats. My new kitchen was ruined, the downstairs neighbour's flat was ruined, there was a massive insurance claim and the downstairs neighbour actually had to move out til it was fixed. Worse still, the upstairs neighbour couldn't be contacted for a week as she refused to answer her phone and we had to write to her (!) so the water stayed on until this random man eventually decided to return just before the council environmental health department were about to break in. Even then, he refused to turn off the water and was really awkward to deal with.
Never heard a single complaint from either of them again!
Anyway, the point is, people are rarely without fault themselves. Find a potential thing that your neighbour does wrong, and next time she complains, go on and on about this thing.