If she is intended to go for an Assasin role, she would need to be reworked a bit.
Assasins need to go close to the enemy, and kill that unit in a short period of time. Right now, her problem is that her main source of damage (Q - Hate Spike) is a hort cooldown, spammable skill, so it is not ideal to assasin a target.
Posible Rework:
P- Dark Frenzy
Evelynn's autoattacks and spell hits on enemy champions grant her a flat movement speed bonus for 3 seconds. This effect stacks up to 4 times.
Q- Hate Spike.
Evelynn fires a line of spikes through a nearby enemy, dealing magic damage to all enemy units in its path. Each fourth Hate Spike will deal bonus damage according of target's missing health and heavily slow target's hit.
W- Shadow Dance
Evelynn removes all slows affecting her and enters stealth for a moderate time. After stealths breaeks, Evelynn gains bonus decaying movement speed and ignores unit collision for a short time.
E- Ravage
Passive: Evelynn restores a slow amount of mana with each auto-attack.
Evelynn slashes a target twice, dealing magical damage and applying on-hit effects with each strike. Evelynn then gains bonus attack speed for 3 seconds.
R- Agony's Embrace
Evelynn impales an enemy champion, dealing magic damage equal to a percentage of their current health and increasing all the damage it receibes by 20% for 6 seconds. All other enemy units in a 250 Radius receive half of that percentage as magic damage.
Evelynn siphons their pain, gaining a shield that grows in strength for each enemy champion hit and lasts up to 6 seconds.
This way she really makes the Assasin playstyle. She starts with Agony's Embrace on the priority target, followed by some E and Q, and finishing the game with the fourth Hate Spike. That is a 6 second window she has to assasinate a target, while enemy team has time to react the coming of an enemy, stealthy assasin (But not like
, there is nothing to do once he jumps on you)