Thoughts:
Passive:
Seems incredibly clunky. Most champs stand still when attacking anyway, and giving her a buff that only applies when not kiting seems like an anti-adc ability. If you want to keep something with the theme of "steady aim" I would suggest granting her a stacking buff upon hitting the same enemy champion, where each hit would either increase her damage against them or increase her range against them.
Q:
Basic attack speed buff, very uninspired. Ashe already has a rapid-fire-arrow type ability, and it's done in an interesting way. Also if you compare it to Tristana, who gets +50% attack speed at rank 1, it's pretty lacking.
W:
Another auto-attack enhancer. Usually you don't want to have more than one of these on a champion, and if you get 2 then one is either on the passive or the ultimate (look at Kai'Sa, Vayne or Xayah for examples). Also, true damage on an ADC with innate attack speed steroid (weak as it is) would get out of hand very quickly. I would suggest moving her true damage to her passive, making it a bit more interactive (say, it only procs when certain conditions are met, or doing something specific) and give her a new ability similar to her current passive (one the one I suggested).
E:
Caitlyn's got one of these. Hers comes with a projectile slow that guarantees her a crit at 1300 range, though, so it's a bit better. If, say, Elora cleansed herself of CC, or became untargetable for a split second while jumping, that would make this ability great (and work better with her ultimate).
R:
Great idea. I imagine her riding something like Ornn ult into battle. If I had one suggestion, however, it would be to allow her to preemptively hop off her boar to allow her to fire it as a sort of projectile, allowing her to stay at a more leisurely distance from the fight, her being a squishy adc. If I had one other, much more minor suggestion, it would be to change the stun to a knock-aside-into-slow effect, like a super-powered Draven E.
