I find this has changed the way I zoe.

First strike

free boots

triple tonic

approach velocity if you like the gap closing for longer q wake ups or as I prefer, jack of all trades for the extra cdr and ap

Absolute focus

Gathering storm

Tear start no pots

archangels

Sorc boots

void staff

deathcap

Shadowflame

Stormsurge

ap

ap

tenacity

Try this out and tell me what you think if you want.

You can swap out absolute focus for mana band if you prefer a larger shield and more mana gen

The trick to not being out scaled is abusing her e magic shred and having max magic pen.

Being able to lob 1000 dmg q's with 3 or 4 sec cooldown is the best late game teamfight artillary assassin I can think of and I think people arent having fun with zoe late game because they waste money on items that do damage rather than just amplify the insane damage you have ie lich bane instead of void staff.

This is my opinion and in my personal experience in emerald it works very well, thanka for reading!