Disclaimer: A somewhat for fun build, and you should pick Conqueror into tanky, brawler-heavy, and melee team comps. Against squishy mages and ranged champions, Electrocute / First Strike (tempo) is the way to go. Eve's playstyle becomes similar to a Cassio with boots, stealth, more one-shot potential, and reliable disengage through ult.

Pros of Conqueror Evelynn: she stacks Conqueror really fast, and with this rune she can actually 1v1 some junglers early game, allowing you to contest scuttle or survive an invade. A lot of people don't expect the increased skirmishing power of Conq eve. With ghost, Eve can stay on her target with conq stacked spamming Q's with increased damage and a bit of healing.

If you get ahead with this build, Eve is even harder to kill, still does a lot of dmg, and is just super annoying. A downside is that building tank items makes her max regen drop to a lower cap.