THIS IS A PTR BUILD. It's decent enough on the live game, but I do not recommend it. 5 more days!
Focused Attack is of course replaced with the new talent.

Cleave is your bread and butter ability. It's cheap, it's low cooldown, it's aoe. This should be used on cooldown unless you're under 100 mana and need to save for a Blink. Without Greater Cleave (which is a crutch talent and should never be used), the range is slightly bigger than your auto attack range. Use Cleave right after an auto attack to be sure it always hits.

Singularity Spike is how you keep up with people whenever Shadow Assault is down. The project is tiny and delayed, so practice with it. If you miss this, you're not killing anything. Very rarely worth using against minions.

Blink is the ability that makes or breaks a Zeratul. Use of Blink with this build is even more important because we are not taking Wormhole. If you make a mistake, you are dead. The majority of your Blink use will be defensive, either to dodge skillshots or to escape. However, do not be afraid to offensively Blink before you get Shadow Assault. If you know you can secure a kill and think you have a reasonable chance of surviving, go for it. But don't overextend into their Uther, eat a stun to the face, watch your target get healed, and then die.

Permanent Cloak gives you a free opener every time as long as you are smart with it and means your roam is very safe and very strong.

Searing Attacks is a massive damage boost. Be sure to activate it pretty much every time you attack a hero.

Berserk is just a flat boost to attack speed and movement speed. Use it like Searing Attacks, but remember its cooldown is more than twice as long. Do not activate it if you're only going to get one or two attacks.

Shadow Assault is your charge. I recommend not using it to start a fight, but using it similar to the way you would use an offensive Blink. This also allows you to pull off some ridiculous jukes if you can bounce like a pinball. Or just the basic Blink away then Shadow Assault in. The duration can be very short in an extended teamfight and once it is on cooldown you're in big trouble. DO NOT ACTIVATE IT TOO EARLY.

The use of your three auto attack buffs is the most important thing you can do. Be sure to keep the activated, and also be sure not to waste them.

Early game you should be roaming. A good way to think about it is to maximize your Seasoned Marksman stacks. Roam to a lane, either kill or severely damage the enemy laner, clear the wave, move on. Always show up to objectives, try to catch enemies roaming between lanes and keep vision on them. Don't overextend, do not die.

Your typical wave clear is Cleave > auto attack higher health minions > Cleave to finish. If you have an ally, it probably will take only one Cleave.

Once laning ends, clear waves whenever you get the chance, but never abandon your team. In teamfights, you're looking for a vulnerable target. Be aware of defensive cooldowns. Jaina's Iceblock, Kael's Arcane Barrier and so on. Do not be afraid to attack a tank. With all your cooldowns up, you shred a tank almost as fast as an assassin. But, an assassin is always a preferable target. Killing an assassin has a much bigger impact.

Zeratul is mostly getting a feel of how and when to flank. Practice, practice, practice. It is a very delicate balance between melting an enemy and getting melted yourself. It has been quite awhile for me, but Shadow Assault Zeratul is very similar to Zed.

Been testing this on PTR. I haven't played Zeratul much since his recent nerf, even though I love the character. With the new talent, I figured it was time to attempt something radically different.
So far, it has been working very well for me on the PTR. However, due to the limited player population, I can't see how it performs in the 4k MMR area, but I am tentatively enthusiastic. Previously, I posted the Clean Kill Kerrigan build, which has become the standard build, so I have fairly good instincts regarding these matters.

No talents can be switched around, unfortunately. Everything is focused on one thing and one thing only and that is ridiculous auto attacks.

Although this build has existed in several forms, it hasn't been very viable, especially compared to the more typical wormhole VP Zeratul build. There are two very big changes for Zeratul with the upcoming patch that I believe will change that.
First, the obvious one. Follow Through is being changed from 75% to 100% and instead of being every ten seconds, it is every third attack. Although this is a direct nerf to the wormhole Zeratul that only gets one or two attacks, this is quite a sizable buff for us, even if we get only the 25% extra damage once. With the way most assassins health pools are, it will take one less auto attack to kill them, due to less overkill. This is why it is very important to ensure your Seasoned Marksman stays stacked, otherwise you WILL end up with enemies having 20-30 health.
Second, with the new scaling changes, Zeratul's auto attacks hit significantly harder in the early levels (relative to before). Before, this build completely destroyed your early game. Now, you have actual assassination potential, even before Shadow Assault.