I played her in a few games recently, and I didn't do all that great with her. How exactly are you supposed to play her? Everyone claims she is just free ELO. Maybe I have bad masteries, runes, or a build going for her. I'm quite good with a majority of the middle champs, but I can't seem to play Eve very well.
Kite like a ***** with Q, sprint away with W when low on health or chase with W when they are low on health, and only use E/melee when you are chasing someone down that is low on health or when you have a shield from you're ult.
Chasing people that run away with no health using her W and securing a kill that would be next to impossible for another teammate to acquire should be a top priority, period.