Objectively the best Vi build you can play atm, good dueling power, ability to one shot squishies, alongside survivability from defensive items and a stronger passive due to hp from said items.
Go Ghostblade before trinity, as its cheaper and gives an early powerspike for a snowball to afford trinity faster.
Go BC instead of Tri if Behind or when you have a heavy ad based team
Feel free to switch for dark harvest, Phase rush is another viable choice
Secondary tree is personal preference but i believe precision is objectively better.

Viable build choice, best when playing with an ad based team needing a beefy frontline.
I'd go black cleaver/Trinity before titanic for the cdr and phage passive.
I prefer black cleaver on a titanic build because cone dmg from Titanic synergizes with black cleaver, for aoe armor reduction, also it will apply the armor break on your main target in 3 AAs instead of 6, so you q aa e + titanic active will insta proc armor break on a target.
Activating titanic hydra correctly can make vi aa twice, followed with an e for fast fast dps, w proc, and armor break from black cleaver.

The hardest build you can play on vi, can one shot squishies with shields and armor on them, but you will die if you make one mistake.
Contrary to popular belief, the build is viable in high elo (dia3-4+), the problem with the build is its suicide nature, realistically if you are ahead, you blow up one or two enemies, burn some of the enemy's summoners and ults and actives, in exchange of your life, how the fight will turn after that is completely dependent on your team.
Build is good in matchups where bruiser build is useless and enemy has hyper carries that your team needs to reach or else they will keep getting poked and lose in all in.

Still viable, assassin vi is better and easier in the midlane than in the jungle, win your lane or shove it, roam bot or top, help team snowball.
start e, poke poke poke, get closer to enemy a minion before you hit level 2,open q and charge it, prepare to q flash after them, q aa e ignite, first blood, congrats, u just won ur lane
max q if u are winning, max e if not so u can shove wave away from your turret, avoid getting poked, and poke back waiting for jungler, ez pz.

Probably the least viable build to do in solo queue atm.
For this build, its all about utility for team, so we are maxing w after q instead of e like usual.

True one shot build in its glory days, but even in its prime it wasnt realistically consistent due to its cost.

was one of my most broken builds, build capped dia 2 85% wr , dead since keystone release and Ardent nerf
hp per level, armor and mr per level runes
blue smite dont upgrade it, frozen mallet first into black cleaver and w max after q
with the mastery that gave teammates hp when they attack a target you cc, build gave all teammates 70-80 hp per second, attack speed and magic dmg on hit.

There are better supports than vi, but vi's peel is godly and her level 2 all in is strong, so some still play her in the support role.
Its best to max w on her.