Build Guide by
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If you go mid lane, get explosive shot first, then rocket jump, then prioritize Buster Shot > Explosive Shot > Rapid Fire > Rocket Jump. Normally if I mid, then I just focus on not getting harassed at all and getting in last hit shots. Normally, if I'm mid, creep killing is very comfortable and it's generally easy to outpace everyone else with Explosive shot for the creep count. If I go sides, I still have the same farming/defensive mindset while being mindful of when my partner wants to go for a kill or a gank. Also be very careful if you're on sides about your positioning, always avoid being positions where you might get harassed even a little bit. Explosive shot makes farming creeps super easy provided you get your timing down. Golden rule is never to go for a last hit if you know you're going to get harassed. Always avoid being in a situation where you might die during the laning phase. Keep in mind your side lanes and keep an eye out for good gank opportunities and moments when your teammate needs help (and only TP or run over there if you know you can help them).
Post-Laning Phase: As you can tell by my summoner spells, I choose flash for a second escape, which combined with Rocket Jump makes you have 2 cushions to correct any mistakes in positioning. Always aim to be at the back of your group fights, plugging shots away at the enemy. Use rocket jump liberally when you need to reposition yourself. Aim to be at the back of the group at all times unless you start chasing fleeing enemies, and even then be sure you can get a kill without trading.
If you end up never dying early and rack up some kills or at least rack up a ton of creeps, you'll be set. Just play safe with controlled moments of aggression. If you find that you're dying on aggressive moves, you're playing on tilt. Roll back on your greed and just keep your cool, and you'll find that you at least win 50% ranked games with Tristana is not by far more than 50%.
For the last item, the second Phantom Dancer is not a set piece. Phantom is definitely a huge DPS boost, but you need to itemize according to what the enemy is building. If anyone has a thornmail, stack up a second Bloodthirster to negate it. If you need armor penetration get Last Whisper (i prefer the raw solo damage increase over Black Cleaver's more group focus applicability).
This item build is purely about finding any possible way to maximize your Damage Per Second with minimal survivability itemization. You don't need the survivability if you always maintain good positioning and are aware of the enemy's movements. Flash and Jump also provide you with 2 escapes. Just play safe and rock hard during group fights. Do not get aggressive early with Trist as none of your summoner spells or your skill sequencing gives you and burst potential until at least Buster Shot.