This is a solution kind of cribbed from Road Runner cartoons...
1. Fashion several cat shapes out of some C4 plastic exlposive bought from the ACME corporation by mail order.
2. Dig a tunnel under his shed (but start it from a neighbours garden).
3. Set up camera to monitor shed remotely.
You can see where this is going...
4. Plant cat shaped explosives under shed and run detonator lines back to tunnel head.
5. Connect detonator lines to switch.
6. Wait till aforementioned thug is in shed with dogs.
7. Press big red button.
8. Problem solved.
This is foolproof as the police will trace the tunnel back to your neighbours house, and arrest them instead of you. So you get rid of the dogs, Mr Thug and those nuisance neigbours as well as having a perfect clip to put on You Tube.
Genius I think you will agree.