At 1st - sorry for my broken english, I hope your eyes will not break until you read my nonsense :3
2nd - Why AP? Because eve assasin -_- we need fast kill enemy, ad tanks eve... if u love ad eve meta - this page is not for you))) i prefer oneshot xD
3rd - Amaizing late game. When u R+hextech+W+E+Q champs slay so quickly, failing to even understand what it was, sometimes say somethink like "WAT???"
Superhardcore late build Evelynn turns into a monster :D . If enemy team don't have hard cc from WW/Malz etc. they lost game)

I use maximum damage, because I think the best defense is attack))

+= here we have a mechanism for making tons of crazy damage and escape.

- This item should appear in your inventory as quickly as possible. This is a huge boost skills + attack damage + physical and magical vampirism + slow with ap dmg. This item turns Evelynn into a deadly weapon.

+ = Tonnnnns of damage :3

= On-hit(+~300x2 on-hit damage for E in late game. Eve E late game hit total ~1500ad+1500ap dmg... pls.. tell me who more op xD)

- goes well with 40% cdr = unstopable eve with spam Q+W

- best magic resist item))) this item will upgrade your hextech+botrk lifesteals.

- let enemy suiside xDDD

- I do not like this item to Evelynn(Lich Bane goes better also), but if the enemy has Seju, Zac, Aatrox, Sion, etc. then buy it is still necessary.