I've found that the builds for Tristana are all situational. I'm winning approximately 4 out of every 5 games(that I don't get solo'd with a 5 man).

I examine the champs I'm facing. if theres a lot of initiators, I'll actually build like this:
Boots+2 HP pots
Zerker Boots
Phage
Catalyst
Frozen Mallet
Banshee's Veil

While this doesn't give the premium damage package that Tristana usually comes with, it will keep her in the fight longer.

If theres not a lot of Initiators/Stunners I'll lean more to this build:
Boots+2HP Pots
Vampiric Sceptre
Ruby Crystal
Zerkers
Zeal
Infinity Edge


If I'm facing a 5 man promote I'll do this:
Boots+2 HP pots
Zerkers Boots
Tiamat
Vampiric Sceptre(for regenning off of creeps and the AOE Damage from promotes)
Zeal
Zeal
Zeal
Getting your Crits and DPS up as high as possible is crucial

If there is a Yi/Jax combo I build:
Speed Boots+2HP pots
Cloth Armor
Vampiric Sceptre
Zerker Boots
Thornmail
Malady
Zeal
Zeal
Zeal

**Of course if the game goes into high end you'll want to get Infinities Edge or a Blood Razor. I like to be able to slow people and come out with a ton of assists and kills though

If you were going against 5 man promote why not get blood razor?
Why would you start with boots and 2 hp pots?

Sword of the Divine allows you to rape jax as long as he doesn't get fed. RJ + Ult means Yi shouldn't be touching you.

I typically get movement speed on Trist when I play her:

Berserker Grieves
Zeal
Vampiric Scepter
Black Cleaver
Malady
Infinity Edge

Of course, mid game I get out dps'ed, but this build makes it possible to harass enemies more effectively early to mid game. Then, late game, when I need the dps, I go dps. Also, if there is a mega-tank on the other team, then you may want to go for Madrid's Bloodrazors... In addition, if there are a lot of dps heros on the other team, the consider going for the frozen mallet sometime mid game.

:/ I like to use my rocket jump for added DPS, the key to beating a 5 man rush is killing the mage creeps because they do the most damage to your turrets. If you focus the Mage row of creeps with a Tiamat plus your corpse explosion you can wipe 5 man promote creeps fast while your team kills the promotes.

I nearly always go:

Dorans shield+hp pot
Berserk greaves
Last whisperer
Vamp scepter(to stay in lane/jungle for runes)
Infinity Edge
(after this make sure to keep yourself agility potted)
Banshee's