Neighbors Dog Broke Into My Property And Injured My Dog, What Legal Action Can Be Taken?

My neighbors 2 dogs had pushed themselves through the fence and got into my yard while my dogs were out. One of his dogs got into a fight with one of my dogs, which it wasn't much of a fight at all since it just rag dolled my small dog. My dog suffered injuries enough to cause me concern, so I took her to the vet. Had to get a stitch, some antibiotics, and cleaned out wounds. Was a 1000$ vet bill at the end of it and the dog is ok. Talked with the neighbor and basically left it as accidents happen, everything is cool just reinforce the fence so the dogs cant get through and also take care of my vet bill. He said he needed some time on payment and that money was tight, I said that was fine just trying to keep the peace between neighbors.

This incident happened Feb 23' and the only money I've received from him was 200$ he gave me when he let me know they were having a big party. Other than that, it's always, "I'm working on it". Since we are over a year ive grown tired of this and just want my money.

Can I take legal action on this matter? I have video proof of his dogs coming into my yard and attacking my dog, copies of the vet bill which i gave a copy to him when the incident happen. We had called the police when the incident happen to get a police report but the police just said to go to the station to fill one out and we never actually did that. We are located in New York