I am confused by this story. Someone fired a bullet, but it was stopped by a cop's belt. The shooter was not charged with attempted murder. Why might that be?
It's important to keep in mind that charges don't really tell us much about what crimes actually occurred. Sometimes cops file charges that aren't justified; sometimes they don't file charges that would be justified. There can be lots of reasons for the gaps between the evidence and the charges. My best guess is that the officers involved don't have quite as much information about his intent as they'd like to have when they go in front of a judge to argue for keeping this guy locked up.
If they're going to hold him for attempted murder, they'll need to present evidence about what he was thinking and demonstrate that he intended to cause the officer's death (ARS 13-1104). That's possible, but it's a lot tougher than what they'd need to show for aggravated assault, which only requires a showing that he "intentionally [placed] another person in reasonable apprehension of imminent physical injury." (ARS 13-1204)
They'll probably bring him up on murder charges, but they probably don't lose much by just booking him now on something easy to prove but serious enough to justify holding him, and then letting a grand jury indict him on the most serious charges.