If you have even one enemy with stun(unless it can rarely be use like ulti) buy Mercury's Treads instead of Berserker's Greaves

The world is not always as civilized as people might think. There are still those who would follow the blackest paths of magic and become corrupted by the darker powers that flow through Runeterra. Shauna Vayne knows this fact well. As a young privileged girl in the heart of Demacia's elite, her father tried to convince her of the constabulary's ever-vigilant eye. Young and nave, she truly believed that her world was one of perfect safety, until one night, when a twisted witch took interest in her father. The malevolent woman overcame her father's conciliar guard, then tortured her family before murdering them. The young Shauna escaped only by hiding herself and then fleeing once the hag had departed, plagued by the screams of her loved ones as she ran. A burning hatred was born in her that day, one that could never be denied.

Vayne was able to take care of herself using her father's money, and she began to train as soon as an instructor would have her as a student. By the time she was a fully grown woman, she had become a grim warrior. However, the fields of battle were not to be her home. Demacia needed a protector, one who hunted those lost to the darkness. Shauna used her family's contacts to become the first Night Hunter, and now her prowess is the stuff of legends. It is said that those who practice the black arts quake when they hear that the Night Hunter is on the prowl. Despite her crusade, Shauna has looked at the League of Legends in horror. There are champions who have clearly lost themselves to the blackest of magics, and who have been embraced within the League even though they should be put down for the safety of all. The time has come for the Night Hunter to execute her secret mission to purge the League of Legends.

Not all shadows are to be feared. At least, if Vayne has her way.

Pros of this build:

• In late game you are fast like the wind-especially with 20 stacks of Sword of the Occult and Youmuu's Ghostblade active.
• nice dmg, critical strike chance and attack speed that will kill your enemy in no time.
• colldown redaction.

Pros of the hero:

• passive that increase speed when attacking and ulti that enhance it.
• stun.
• short stealth.
• Multi use Tumble with only 2 sec colldown before colldown redaction.
• Her ]Silver Bolts does nice dmg.

Cons of the hero

• squishy.
• bad vs stun.

Cons of the build:

• no life steal.
• running wont help against stun.
• almost no defensive items.
• Hard to gather and keep Sword of the Occult Sword of the Occult stacks.

Hard keeping the stacks or killing the enemies? IF you dont want to buy sword of Occult or want to sell it you can buy those(more expensive) items that can be bought by the end(because you have almost nothing left to buy and you want to switch the Sword of the Occult) or buy when I recommend to(if you don't want to buy the Sword of the Occult-then buy first Dagger or dorans blade instead of Long Sword) or switch these items with other items you dont like in my build:
Madred's Bloodrazor: the most recommended replacement item great dps item but very expensive and its passive wont increase critical strike bonus dmg and her abilities bonus dmg. after Trinity Force
Frozen Mallet: great item that gives you health and slow, buy after Trinity Force.
Hexdrinker: The cheapest of the replacement items-gives some attack dmg and nice passive that will help you stay alive vs ap heroes. buy after Youmuu's Ghostblade if its argent or after Trinity Force.
The Bloodthirster:the best lifesteal item that gives you bonus dmg too, but a little bit hard to keep stacks. buy after Trinity Force
The Black Cleaver: nice dps bonus and good vs stacked armor champs. buy after Trinity Force
Last Whisper:some dmg and good vs very hight armored. buy at the end.

Phantom Dancer:if you want you can buy another Phantom Dancer for almost 100% critical chance and movement speed but this is not recommended because there are many other great items. buy at the end.
Banshee's Veil:great defensive item vs annoying stun abilities, gives you health mana and MR. buy at the end.

I start with Long Sword for dmg and for the Sword of the Occult. another option to start with dagger if you want to buy Berserker's Greaves. I don't buy dorans blade beacuse you want to get the Sword of the Occult fast. but as I said if you don't want to buy the Sword of the Occult you can start with dorans blade.
Then I buy Berserker's Greaves for movement and attack speed or Mercury's Treads against stun.
After that I buy the Sword of the Occult for more dmg and its nice bonus at 20 stacks-110 dmg and 15% movement speed. Its pretty cheap too.( don't buy it if you are getting killed a lot or you don't kill(see Instead of Sword of the Occult or other good items chapter)).
After that I buy Sheen because of its passive that gives you bonus dmg after Tumble.
In that time I go to the more "heavy" items: I buy Youmuu's Ghostblade-Not many include that item in Vayne but it have helpful cooldown redaction, critical chance, some dmg and an very very nice active that give you movement and attack speed as long as you attack the enemy, because when you use the active even champs with movement ability will find it hard to run from you with her passive and this active and when in fight the AC bonus is very helpful.
Then I buy the Trinity Force mainly to enhance the sheen effect but beacuse of its slow chance, movement speed, AC, dmg, and critical chance(it gives health and mana bonus too)-enough reasons for the most expensive item in lol to be a core item for her.
Now you should have enough critical chance(from Youmuu's Ghostblade and Trinity Force) to buy Infinity Edge-For more critical dmg. Then most of your attacks will be critical. and after trumble you could do very hight dmg-trumble bonus+trinity force bonus+critical bonus!.
In the end I take Elixir of Agility and phantom dancer for more critical chance.
you could sell the Sword of the Occult to buy another item from the chapter Instead of Sword of the Occult or other good items if its hard for you to remain at 20 stacks since you have nothing left to do with the money except to buy consumables.

The Black Cleaver:
I buy Youmuu's Ghostblade instead beacuse even if The Black Cleaver is a little bit better at dps and penetrate more armor, Youmuu's Ghostblade have cooldown reduction, critical strike chance and very nice active.
Madred's Bloodrazor:
A.no critical strike chance.
B.very expensive.
C.It have a very nice passive but Tumble,Condemn and critical strike dmg are based on physical dmg and not magic dmg.