heron 7 might and sprite queen 6 vs Nidalee 4 might noxian emissary 2 might kayle 9 might. can heron and sprite queen kill Kayle with 9 might and leave Nidalee on the field instead

Yes — the attacker chooses assignment order and can kill Kayle while leaving Nidalee alive.

Heron + Sprite Queen sum to 13 Might (Rule 465.2). Assigning player goes unit-by-unit, finishing lethal on each before moving on: put 9 on Kayle (lethal), 2 on Noxian Emissary (lethal), then the remaining 2 on Nidalee. 2 damage is non-lethal against her 4 Might, so she survives (and that damage heals in Combat Cleanup anyway). You may not skip Emissary to spare Nidalee and also kill Kayle, since all 13 damage must be assigned — but killing Kayle + Emissary and leaving Nidalee at 2 is fully legal.

Caveat: the defender's 15 Might still has to be assigned and will kill both Heron (7) and Sprite Queen (6). That leaves Nidalee as the sole survivor, so the defender wins the showdown and her "when I win a combat, draw 1" still triggers (Rule 461). Leaving her alive doesn't avoid that outcome.

Rule ref: 465.2.c.