Burst damage and snowball potential.
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.
9% attack speed, 9 ability power or 5 attack damage
Takedowns restore health and grant bonus gold.
Deal 7% more damage to low health champions. Gain AD/AP after kills or assists.
The extra bit of burst damage from Electrocute allows you to quickly execute enemy champions with your [R]->[Q]->[E] combo.
The bonus Lethality gained from casting [Q] and [R] provides even more damage when hunting an enemy champion.
Eyeball Collection is a solid choice here for increasing your damage. Because you're playing a very assassin-heavy build/playstyle, you want to get ahead and snowball the game
Relentless Hunter lets you zoom around the map to find fights and kills and the drop of a hat.
If you're opting to build Lethality active items, Ingenious Hunter can be good here to use those actives more often and sweep more wards.
Triumph's extra burst of healing on kills/assists allows you to play aggressively by diving the back-line, killing your target, and getting out safely thanks to the extra bit of health back.
Coup De Grace is the go-to rune for extra damage when looking to burst/assassinate squishy back-line targets as quickly as possible.