Complex sentence: Despite falling short of the Hot 100, "Applause" did peak at 16 on the Dance/Electronic Songs chart, and entered the U.S. Pop Songs Chart at number 20; the highest debut on that chart, by a solo female artist, in 2013.
Split into simpler sentences: Despite falling short of the Hot 100, "Applause" did peak at 16 on the Dance/Electronic Songs chart. Following the single's release, it rocketed to number 20 on the U.S. Pop Songs Chart and became the highest debut on that chart by a solo female artist in 2013.