Target is winning back shoppers. Now it faces a big test.

A Target store in Brooklyn earlier this month. Michael M. Santiago/Getty Images Back-to-school shopping is in full swing at Target, representing a key moment to win back shoppers. A successful season requires overcoming several challenges the retailer has struggled with recently. The retailer's turnaround continues, with second-quarter sales up 5.3% and comp sales rising 3.8%. Target's bid to win back shoppers is gaining momentum as it tackles one of the most important shopping seasons of the…