squishy_sultana

It isn't to do with the Firesweep weapon per se. You can observe this on the Normal difficulty version of this GHB, where the Red Sword Flier isn't using a Firesweep Sword. To roughly describe it: When there are no immediate attack targets for the AI team, units without assist skills (the green ones) typically move first. Of those, melee units have priority over ranged ones. So on Infernal and Abyssal, the Red Sword Flier and Blue Lance Cavalry moves before the Green Bow Infantry. The Red Flier moves before the Blue Cavalry because it is closer to your units. A singer/dancer's Sing/Dance skill has priority over this, but it needs a viable target. In the case of this map, The Red Sword Flier moves first. Having ended their move within reach of Azura's Gray Waves reach, they are a viable target, so she uses it. After the Red Sword Flier's 2nd move, the Blue Lance Cavalry then moves, followed by the Green Bow Infantry.

Mind if I asked if you have worked out a solution since this post? Tentatively speaking, I think you can clear the cavalry challenge with the units you've listed. I don't mind having a look when the map comes back if you still need help with it.