What the achievement asks
Defeat creatures empowered with elemental air during a storm event in The Azure Span. Account-wide.
That means a Thunderstorm in that particular zone, and it is the pairing that makes this branch long: sixteen achievements, four elements across four zones, and you do not choose which one turns up.
Only the imbued creatures count
Not everything inside a Primal Storm counts. Only creatures carrying Elementally Imbued do, and killing everything else in the area gives you nothing.
Check for the buff before you commit to a pull. It is the single most common reason a storm feels like it gave no progress.
The clock
Primal Storms run on a three-hour cycle: active for two hours, then an hour with nothing. There is no fixed rotation of element or zone, which is what makes the sixteen combinations a matter of patience rather than planning.
The Waking Shores and the Azure Span have more storm sites than the other two zones, so they come up more often. The scarce combinations are the ones in Thaldraszus and the Ohn'ahran Plains, and they are what you will still be waiting on at the end.
Check a storm timer rather than flying out to look. Turning up an hour into a two-hour window still leaves plenty of time; turning up during the dead hour wastes the trip.
Do all four elements at once when you can
Every storm you attend also feeds Stormed Off, which wants eight of the rares that spawn in them, and Elemental Overload, which wants 5,000 Elemental Overflow. Neither cares which element or zone, so nothing you do in a storm is ever wasted.
Where it fits
One of four under Chasing Storms in Thaldraszus and the Ohn'ahran Plains, part of Storm Chaser and Into the Storm, and so of A World Awoken.