This question can be a little difficult to answer because of varying skill levels in this game.
From personal experience, she seems to be somewhat viable until gold ELO. At that point, teamfights are better coordinated and the problem with AP Tristana is that if she uses all her skills and doesn't get a kill, then she will just be on cooldowns for most of the teamfight, which is extremely detrimental to your team.
In teamfights, don't stupidly jump into the enemy and try to get a kill. Wait for an opening when your team is already fighting - Go in an try to kill whoever needs to be prioritized. Usually I go for the ADC, but sometimes you will not be presented with that opportunity. Kill whoever needs to die first.
Rocket Jump towards target >>> Before Landing, Use Deathfire Grasp for the % Damage (Set it to Smartcast in Options >>> Ignite >>> Fire Explosive Shot to counter Lifesteal/Healing >>> Use Buster Shot if necessary.
Proc your Lich Bane passive whenever you can. Also, remember that if you get a kill, your Rocket Jump refreshes.