Do you know what it is, or what it is slang for?
I did a web search of 'tilly hawk' and found the site below. I'm a birder but wasn't familiar w the term, apparently in some areas (USA anyhow) this is another name for a sparrowhawk which is a kestrel (small falcon). Thanks, I love picking up a new tidbit.=:]
http://theclogalmanac.blogspot.com/2005/...
I don't know of a tilly hawk, but I do know of a falcon, that has a call which sounds like "killy." The American Kestrel is a falcon which makes a "klee klee klee" sound. This sounds like killy, which is probably what you're referring to in your question.