Need help border Training a Cat .

Some years ago I had the same situation, what I did was that I fix this spcecial laminate that many cars use for privacy (it can be seen from the inside but not from the outside where it looks like a mirror) in two of the four windows of my apartment.
I didn't want to eliminate one of the greatest pleasures of my cat, watch through the window.

That seems like a good idea.

I had a similar problem when I moved house. My new neighbour wasn't too pleased to have cats on her lawn etc. Cat repellent didn't work. What my wife and I did then was, we bought a pair of those high power water guns and when we let the cats (10 of them) out, we waited along our neighbour's fence and sprayed any cat that got near the border (didn't hit them directly though).

After about 3 days of this, it seems to have helped because our neighbour hasn't been over to complain again since.

Now the water guns are on standby because every now and then one or two of them may need reminding.

Elimating one or more of the windows sounds like a really good idea. Especially since cats love to look outside all the time.