Analysis for the current Tristana 5.4/5.5 and recommendations
Currently Tristana is in a rough spot. Her reported win rates and damage dealt are some of the lowest among all ADCs currently. I believe I have spotted two of her most problematic areas, her range and her attack speed.
Tristana, even after her rework, is still a very traditional ADC. She likes to shoot at people (who have her Explosive Charge) at range and only jump in if it will secure a kill. The problem is her range is at odds with her kit until late game. Tristana starts out with 550 range, the same as Vayne. However, while Vayne has a number of tools that make her a great assassin at this range, a stun, a low CD dash, true damage, Tristana has none of these. That is fine due to trying to make her early game difficult for late game rewards. The problem is that Tristana only gains 7 range per level from her original 9. This causes Tristana to only reach classic ADC range of 600 by level 9/10. This makes Tristana's job much more difficult as games are designed to end much sooner and cannot achieve her full range.
Speaking of late game, it isn't much better for her. Tristana reaches “long” ADC range at about level 15/16 marked by Caitlyn, about a standard game should be ending and capping out a 669 range. For stacking to get to 18, Tristana still does not have the longest range, that is held by Jinx at level 9 with 700 with Fishbones. While it does cost Jinx some mana, it also gives her 10% bonus AD, and a 150 radius splash per hit.
The second problem is Tristana's attack speed scaling. Early on her attack speed on par with Ashe, however, as the game continues, the poor scaling causes her to end up ~.3 behind Ashe. Jinx has a similar scaling, if starting slightly lower, but is covered by Pow-Pow, which allows her to hold a steady +1.0 attack speed at no cost. Tristana on the other hand needs to use her Rapid Fire ability to deal more consistent damage, but only last 5 seconds and has a 20 second cooldown. If this is able to hit a target with an Explosive Charge, the cooldown will be reduced by up to 5, but her limited range makes that problematic and even then, it will not be back up for the remainder of a skirmish.
I would recommend increasing Tristana's attack speed growth and see how it improves her. If that is not enough, look into increasing the scaling for her passive.
I would like to thank Frightning with his help on the math for attack speed.
TLDR: Tristana's attack speed growth and passive scaling feel too low and should be considered for buffs.