The sentence that is correctly punctuated with a colon is,
"I have finally mastered new tricks for the half-pipe: the pop tart, the barrel roll, and the Miller flip."
A Colon can be used instead of a semi-colon between the two independent clauses. the clauses are meaningful but to some extent incomplete. The clause after the colon explains, expands or illustrates the preceding clause. In the above sentence, the first independent clause is a complete and independent clause and the second clause is giving more detail about the tricks which the person has mastered on.