As someone who main evelynn i have to say that the only help that evelynn need is on her base stats!
Right now Evelynn have one of the smallest Base stats in the game and that make no sense!!!
I mean she have low MS because she have a self buff speed...ok.....what? yi/gp/vi and all the other champs have low CD DASHES and self speed and they dont have such a low MS!!
Then her base HP and hp per lvl...again way too low!! she is marked as "assasin" but other "assasins" have more base hp than evelynn...it make no sense a melee assasin to have lower hp than a range assasin (Ahri)
Her armor base armor would easily need some help i mean evelynn is a jungler right"? well with evelynn you need to have always 4 pots with you other wise you cant clear the jungle without end up with less than half hp!! so yeah some armor buffs would be good...
now i know that evelynn have a shield but her shield is on her ultimate abilty that have 150 second CD and when you have VI that have gap closer and a shield ON HER passive and have better base stats then you know that its something wrong with that!!
So for me Evelynn only need some buff to her base stats in that way she would not become broken but she wouldnt be useless ether!! Because lets face it you cant 1vs1 anyone special in early game...and that wrong..when all other junglers can easily 1vs1 everyone in the game!