In order to challenge a law in court, one must demonstrate that the law in question is in conflict with an existing law, and the conflict must be resolved by the court, who then must rule. The resolution can be a full overturn, or explain that there is no conflict, or anything in between.
The primary approach expected to challenge SB1070 is the preemption argument. American Civil Liberties Union (ACLU) and some constitution law scholars claim that Arizona law is preempted by Federal immigration laws. The US Constitution specified that only Federal government may enact and enforce immigration laws, not the states. Thus, Arizona law is preempted by the Federal laws on immigration.
The secondary approach is the rights argument, specifically 14th Amendment, in that States shall pass no law abridging any citizen or lawful resident of their Federally guaranteed rights. Their argument would be that the normal citizen or legal resident rights are violated by SB1070, and therefore SB1070 must be repealed.