Pure assassination and map presence.
Burst damage and target access
Hitting a champion with 3 separate attacks or abilities in 2s deals bonus adaptive damage.
Gain a burst of Lethality and Magic Penetration after using a dash, leap, blink, teleport, or on leaving stealth.
Collect eyeballs for champion and ward takedowns. Gain permanent AD or AP, Adaptive for each eyeball plus bonus upon collection completion.
Unique champion takedowns grant permanent out of combat MS.
+18 Ability Power or +11 Attack Damage, Adaptive
Gain cooldown reduction and max cooldown reduction on your ultimate. This is increased further each time you use your ultimate, up to a maximum.
Gain 4% extra MS. Gain extra AP or AD, based on your bonus MS, Adaptive.
Evelynn is able to easily proc Electrocute when coming out of stealth with a [W]->[Q]->[Q] combo for an extra burst of damage to finish her target.
Exiting Stealth grants the Sudden Impact bonus Magic Penetration that Eve can use to assassinate the enemy champion.
Clearing wards is a key part of a jungler's position. Pair that with assassination potential and you'll be racking of plenty of bonus Ability Power to snowball the game.
Movement Speed is a key aspect to getting around the map to meet and initiate fights.
Evelynn's [R] offers massive offensive power with it high base execution damage, and great defensive utility with it's ability to quickly blink you over a wall to get away.
More [R]s means more kill and more chances to live.
The bonus Movement Speed from Celerity allows you to more quickly and effectively clear the jungle so you can properly position for ganks.