Perhaps protecting your property with lights, fencing, and cameras might help, or actually speaking to the lawful authorities about your legal options would be a better solution than your potentially illegal action of "shooting the fucker".
Each state, with the exception of North Carolina, permits citizen arrests if the commission of a felony is witnessed by the arresting citizen, or when a citizen is asked to assist in the apprehension of a suspect by police. The application of state laws varies widely with respect to misdemeanors, breaches of the peace, and felonies not witnessed by the arresting party. For example, Arizona law allows a citizen's arrest if the arrestor has personally witnessed the offense occurring.
http://en.wikipedia.org/wiki/Citizen%27 ... ted_States
In Canada we have this:
Section 494. (Criminal Code)
(2) ARREST BY OWNER, ETC., OF PROPERTY
Anyone who is
(a) the owner or a person in lawful possession of property, or
(b) a person authorized by the owner or by a person in lawful possession of property
may arrest without warrant a person whom he finds committing a criminal offence on or in relation to that property.
You have options, but if you decide not to use them, that's not Anarcho-Tyranny.