Im just a Zeri main who was one of the first players who discovered zeri trinity force after she came on pbe , then i started thinking about first ap marksman, dealing magic dmg from aa,lich bane allows it because of the same mechanic that has trinity force, because of the same mechanic uyou can't build both aswell, now im tired of playing against tristana, lucian and others and made mid lane zeri viable.

zeri is able to oneshot enemies also kite like adc, but she can be also oneshoted
cons: squishy , long cd dash, weak without R, hard to land w, low range of ap q, low aa dmg in early game, low dmg overall, low movespeed
pros:her qwr oneshots squishy champions, w can be aoe, she has free none mana cost massive dmg early ability, great scaling high kite potential, good mobility, much slows, well working with lethal tempo, hard to catch

passive

Zeri Shields herself for 60% of the damage she deals to enemy Shields and gains 10% Move Speed for 3 seconds whenever she receives a Shield.

burst fire

Range: 825 Cooldown: 1.52 Passive: Zeri's Attacks are treated as Abilities and can be charged up by moving and casting this ability. Uncharged Attacks deal (10-25^ + 3% AP) magic damage, increased to (60-150^ + 18% AP) damage vs. enemies below 35% health, and consume some charge. A fully charged Attack deals (90-200^ +80% AP) + (3%-15%^) max Health magic damage, Slows by 18/26/34/42/50% for 1 seconds, and consumes all charge. Active: This Ability is treated as an Attack. Zeri fires a burst of 7 rounds that deals 7/9/11/13/15 (+110/112.5/115/117.5/120% AD) physical damage to the first enemy hit. Passive damage applies Ability effects and cannot crit or apply on-hit effects Active damage can crit, apply on-hit effects once per target, and hit anything that an Attack can. The Cooldown and cast time scale down with Attack Speed (max 1.5 attacks per second). 60% of excess Attack Speed is converted into Attack Damage.

ultrashock laser

Range: 1200 / 1500 Cooldown: 10 Cost: 50 / 60 / 70 / 80 / 90 Zeri fires an electric pulse that deals 10/45/80/115/150 (+1.2 of attack damage) (+70% of ability power) magic damage and Slows the first enemy hit by 30/40/50/60/70% for 1/1.25/1.5/1.75/2 seconds. If the pulse hits terrain, it expands into a laser that applies the effects in an area.

spark surge

Range: 300 Cooldown: 28 / 26.5 / 25 / 23.5 / 22 Cost: 80 Zeri dashes a short distance and vaults over any terrain she touches, greatly extending the dash range. Her next 3 shots of Burst Fire pierce, dealing 80/85/90/95/100% damage to enemies after the first. Hitting a champion with an Attack or Ability reduces this Ability's cooldown by 1 seconds.

LIGHTNING CRASH

Range: 825 Cooldown: 120 / 95 / 70 Cost: 100 Zeri discharges a nova of electricity, dealing 150/250/350 (+ 80% bonus AD) (+ 80% AP) magic damage to nearby enemies and gaining 3 stacks of Overcharge for each champion hit for 6 seconds. Each stack grants 2% Move Speed. Hitting an enemy champion with an Attack or Ability adds a stack of Overcharge and refreshes its duration by 2 seconds. While Overcharged Zeri also gains 30% Attack Speed, 10/15/20 (+ 15% AP) magic damage On-Hit, and Burst Fire becomes a faster triple shot that chains the bonus magic damage and 25% AD physical damage to nearby enemies.

barrier - great against champions like katarina or talon which basically oneshots you before you click exhaust on them
ignite - if you win matchup (rare) you can go ignite for more dmg
exhaust - if enemies are killing you fast and don't have instant blinks near you, you can go exhaust and get away when they will have chance to kill you

which rune?

Great overall rune for helping extend Zeri’s Q Burst Fire range. During teamfights it is fairly easy to stack up with your long range Q Burst Fire. Zeri loves extended trades, especially with her ult Lightning Crash that grants her more MS based on the number of stacks. Lethal Tempo synergizes well with her ult Lightning Crash, helping chase down fleeing enemies, or to reach backlines with the extended Q Burst Fire range and the increased MS. As Zeri doesn’t often struggle with mana issues, Triumph is a solid rune to take for those close teamfights, providing HP to keep you safe. as ap zeri you need aa speed , this rune provide it. coup de grace is working well against bruisers and tanks, however it is also good for oneshoting, if you want you can go cut down against tanky enemies. this rune provides you lower cd on items such as lich banes where your main dmg comes from.

ap mythic on zeri is almost useless, she doesnt have any dmg from them, riftmaker gives you small true dmg and small healing, when nigh harvester gives you little more burst dmg, but still it istn such usefull like on katarina, so you should go mythic after building core items (lich bane and nashor tooth + boots) when you wil just get more ap

lich bane procs every physicall q so you have free dmg and has scaling ap so in late game you can deal 450~ dmg from just this one item, additionally nashor tooth deals dmg every attack so you have another scaling ap dmg on aa

depending on matchup you can choose boots, if you are facing warwick, trundle, tahm kench etc. go swifftness anty slow and more ms, if enemies are full ad assassins like talon you can go plated steelcaps, if enemies are most ap and good cc try mercenary, commonly you should take boots for aa spd, ionian are usefull only when you are really fed, for faster w

in early game try to just farm safe, you will lose most matchups so roam with jg, try to have good wave managment to have good cs and try to not 1v1 enemy unless your matchup is good

after you have got first item and boots, start teamfighting more, your power is in teamfights when you have good position you can kill enemies well and they can't really do anything about that (exceptions - evelynn, talon , kassadin etc.)

after you are full build all you have to do is having good position and killing enemies depending on your items you can all in and make pentakill - why not
keep vision great to make enemies fear you more than fiddlestick :)

working on ...

good positioning means just being in position where enemy players cant takedown you, you can hide behind wall or shoot from bushes, also going in, on their backline after your team all in into enemy team melee and oneshoting squishy targets is also good decision if noone of them counters you (tristana, lucian etc.), place blue wards after lvl. 9 so you can have more vision and after buying core, boots and mythic you can start buying control wards too.