How would a judge who is a strict constructionist interpret the 2nd Amendment in the face of an argument by a Constitutional attorney who asserts...

The strict constructionist would dismantle the constitutional attorney's argument by using the legal precedent, District of Columbia v. Heller, the Supreme Court's 2008 decision which found, by a 5-4 vote, that the District of Columbia's ban on handguns was unconstitutional. The Heller decision was the first major ruling on the Second Amendment since 1939 (United States v. Miller). 

I will assume the voice of such a judge:

"While it is true that the well-known prefatory clause, 'a well-regulated militia,' did express a purpose that was particular to its time, according to the Court, 'it [still] does not limit or expand the second part': 'the right of the people to keep and bear arms shall not be infringed.' Moreover, the prefatory clause acts as an anti-Federalist check on a government that could revert to tyranny. The clause acts to deny Congress the power 'to abridge the ancient right of individuals to keep and bear arms...' 

"Moreover, at the time that the Constitution was ratified, there were state constitutions that provided citizens with 'arms-bearing rights.' 

"While the Second Amendment does allow for limitations, such as 'longstanding prohibitions on the possession of firearms by felons and the mentally ill,' it contains no language that prohibits the possession of arms altogether."