First of all, Moïra will try to identify what her adversary is, through a Knwoledge (Nature) check, with a +5 bonus from Collector of Stories.
Rolled 1d20+27 : 20 + 27, total 47
Then, she'll use her Pixie Invisibily to go, you guess it, invisible, as a free action. Considering that she is invisible, and she also got Hide In plain Sight, she'll try to hide at the end of her round.
She now uses 3 inspiration points for one additional move action, used to fly to the left of her target and backward, at the maximum of her range - that is 50 feet.
Standard action : she'll use one of her Pixie SLA to
Entangle the Bat man she is facing. the Will save DC is 31.
Move Action : she'll Aim, thanks to Accelerated Aim, for a single attack. She 'll spend 6 inspiration points, 3 to add her intelligence bonus to hit for 14 rounds, and the same to damage for the same duration.
thanks to her splitting airifle, that means two attacks. crit on a nat 20, x3.
first attack
Rolled 1d20+48 : 7 + 48, total 55
first attack damage roll (force damage)
Rolled 1d8+15 : 1 + 15, total 16
Aim bonus damage on first attack
Rolled 7d6 : 4, 5, 3, 5, 6, 1, 3, total 27
second attack
Rolled 1d20+48 : 17 + 48, total 65
second attack damage roll (force damage)
Rolled 1d8+7 : 2 + 7, total 9
Aim bonus damage on second attack
Rolled 7d6 : 4, 5, 1, 5, 2, 2, 3, total 22
last roll, to see if she hides successfully.
hide check
Rolled 1d20+54 : 15 + 54, total 69