What principle does the us supreme court apply when it declares an act of congress unconstitutional?

The principle is checks and balances, it ensures that none of the three branches (Executive, Judiciary, and Legislative) gain too much power.

Opposition to the nra came to a head in 1935, when the conservative supreme court declared the agency unconstitutional, claiming the nra gave the executive branch regulatory powers that belonged exclusively to congress. this decision began a series of court decisions that overturned key elements of the new deal.