AP Tristana is the rarest(reasonably viable) build I've seen in the time I've played. The reason? People don't think she's viable.
This works for someone who knows how to play an AP Tristana though as enemy players don't even know what hit them when you start nuking them down from full to 0.
AP Tristana is definitely one of the strongest early game nukers and gankers I've seen and is possibly overpowered during this stage of the game. Her full combo can take out heroes in one go before they even react. The problem is that once the game goes into endgame her viability takes a hit.
I've had alot of lashback from playing AP Tristana so don't expect everyone to be supportive and leave you alone to build what you want. In those games you don't do well they'll call you the worst of things to stick the loss on to your unorthodox build but you'll know that AP Tristana isn't too bad when you get scores like 28/4/3.
I'd like to say that I'm an objective person so I won't turn a blind eye to the problems with AP Tristana. If you choose to play AP Tristana you will get amazing Kill/Death ratios. You will get amazing streaks. You will do amazing burst damage. But what you won't do is win all your games.
The problem with AP Tristana is that your initial burst damage is all you can do, and you will kill at least one person with that burst.
But this isn't enough to win games on Summoners Rift (completely different story on Twisted Treeline, but I'll get to that later).
As a DPS and Carry you need to kill more than just one person to win team battles. DPS champions need to keep dishing out the damage. As long as they live they will keep knocking down champions after champions.
As an AP Tristana you will kill only one person and then put out piddly sustained dps afterwards, no matter if the team battle was stacked in the enemy's favour or yours.
It's fun entering an enemy battle completely out numbered and killing one of them but this is also the big downside of playing AP Tristana.
You don't contribute enough to team battles. You need to rely on your team mates to finish off the remaining champions while you twiddle your thumbs waiting for your cooldowns to return. Prepare yourself to lose games even when your personal score is 30/5/5.
What does Tristana take from AP?
I've had this asked to me many times when questioned about an AP build.
Rapid Fire does not scale with AP but your other 3 spells do, and they do well. I'll get into depth about this later but 3 spells scaling well with AP already makes a champion viable for an AP build in my books.
Tristana fires her weapon rapidly, increasing Tristana's attack speed by 30 / 45 / 60 / 75 / 90% for 7seconds.
Cooldown: 20 seconds
Cost: 100 Mana
This spell is pretty much your deadweight spell in the early game phase. I occasionally don't level it at all until everything else is maxed but it's a good idea to put at least one point into it for pushing towers or just a bit of extra DPS. Once you build your Lich Bane you'll be using this for an extra Lich Bane proc.
Tristana fires at the ground to propel herself to target location, dealing 70 / 115 / 160 / 205 / 250(+0.8 per ability power) magic damage and slowing surrounding units by 60% for 2.5 seconds when she lands. On kill or assist, Rocket Jump's cooldown resets.
Cooldown: 12 seconds
Cost: 100 Mana
Your bread and butter spell. This spell takes 0.8 damage from each point of AP so it scales pretty well. An extremely useful skill. You'll be using it to initiate, nuke, farm, chase, escape, reposition, eat, sleep, etc. Everything you can think of. Max this spell first. This spell will wipe out waves of creeps in one go.
The interesting thing about this spell is that the cooldown resets whenever you get an assist or kill. This opens up interesting strategies such as jumping into a team of champions, nuking the living daylights out of a champion at around 50% hp and then jumping back to safety. Very risky but sure as hell is fun. Learn to use this part of the spell. Keeping an eye on a kill so you can plan your next Rocket Jump will be a big factor in battle.
Also, make sure that if it's not on cooldown before an enemy champion dies, put it on cooldown. Unless you need the mana.
Passive: While Explosive Shot is ready to cast, enemies explode when slain by Tristana's attacks, dealing30 / 50 / 70 / 90 / 110 magic damage to nearby enemies.
Active: Explosive Shot rends target enemy, reducing healing and health regeneration by 50% and dealing 25 (+0.1 per ability power) Magic Damage per second.
Lasts 4 / 5 / 6 / 7 / 8 seconds.
Cooldown: 16 seconds
Cost: 50 / 60 / 70 / 80 / 90 Mana
This spell is extremely underrated. The main purpose you'll be using this spell is not for it's farming capabilities (for which Rocket Jump already nicely covers) but for its damage and anti-healing aspect.
This spell takes 0.1 damage from each point of AP per tick, which at a first glance is pretty underwhelming but this spell ticks every second for 8 seconds, which means that for each cast of the spell it in fact takes 0.8 damage from each point of AP. when you get your SoulStealer and Sorceror Boots alone you'll be looking at a total of about 350 damage all up.
Granted this is still not an amazing skill on damage alone but added with the anti-healing debuff it becomes an effective spell rather than the wasted skill many people perceive it as. Plan for heals, many people take Heal as a summoner spell so lay this debuff on them when their hp is getting low when you're expecting an incoming heal.
Tristana fires a massive cannonball at an enemy unit. This deals 300 / 400 / 500 (+1.5 per ability power) magic damage and knocks surrounding units back 600 / 800 / 1,000 distance.
Cooldown: 60 seconds
Cost: 150 Mana
This is the big nuke which will separate you from your physical DPS counterpart. This spell takes a whopping 1.5 points of damage from each stat of AP allowing you to reach damage levels comparative to Veigar's ultimate. Whats more is that it's only on a 60 second cooldown. Gank at every opportunity when this comes off cooldown. Gank even if it's not completely off cooldown, more often than not it'll become available during the battle or while your travelling there.
This will be your finishing spell, enemies will WTF at it's damage and rage at being killed at half hp with a single spell.
Be careful that if you plan to use this to deal the finishing blow, make sure the damage is more than enough to do the job, punting the enemy out of danger because you didn't kill them with it and seeing them get away with the tinyiest bit of hp can bring the hardiest of players to the depths of despair (not to mention the rage you will get from your team mates).
Keep in mind that although you want to keep this spell for finishing blows, using it like a normal Buster Shot to reposition the enemy or save an ally is still important, don't be too stingy with it.
EXTREMELY IMPORTANT. This spell adds 200-500 points of pure damage to your burst combo, and AP Tristana is all about burst damage. This can guarantee a kill from a champion with full HP every 2 minutes. When used with Explosive shot it becomes almost as good as straight up damage due to their health regeneration and incoming healing being stunted by the debuff. Use it, spam it, love it.
Everyone knows Flash, everyone takes Flash. The good thing about having a blink as a summoner spell is that you can use it no matter what champion you pick. The bad thing about Flash is that everyone else has it.
You'll be relying on your Rocket Jump to do damage and very often you'll find yourself in many sticky situations you'll need to get out of ASAP with Rocket Jump on cooldown (more often than not, you may also be in these situations because of Rocket Jump). Flash gets you out of these and can almost certainly save your life, or guarantee a chase kill with each use.
Flash's unappreciated little brother. Low CD, not as reliable, but better for long term chases and running away if you can escape their initial grasp(which you can pretty often with Rocket Jump).
Can also save lives or give you enough hp to finish off a kill, you don't need much hp to kill someone with your combo and many times I've used heal right when I've lured an enemy and given him the good ol' 1-2-3 nuke combo. Won't always get you out of bad situations like Flash does but it's use during the initial laning game phase is indispensible
Personally I run with Flash and Ignite, with Heal on occasion(read: while I'm below level 12)
Stack Force(AP per level) on your runes, with Magic Penetration on your red.
If you like AP more than Magic Penetration then you may also stack AP on your Red Runes due to the extra damage on each LichBane proc. This only applies to Lich bane and the difference is pretty marginable though.
I like running full Utility with Offense up to Archaic Knowledge (15% Magic Penetration) due to the reduced cooldown on Summoner spells (such as Ignite, also Ignite and then again Ignite) but going full Offense for the extra damage as well as the Ignite Mastery is also a very tempting option. The problem with full Offense is that the later levels of the tree really doesn't do much for your spells.
Philosopher's stone - I need to stress that your getting this not because it's a Gold-Per-10 item, (though it's a nice bonus) you really need the regeneration it provides to stay out there and gank. Feel free to sell this item after you've built your Lich Bane.
Boots - Leave these as level one boots until later, the extra MS pales in comparison to getting your SoulStealer 550 gold faster.
Mejai's SoulStealer - You'll be ganking and delivering finishing blows with Buster Shot like crazy at early game so you'll be able to fill this up to its 140 AP in absolutely no time. The mana for each kill is also important since it's what you need to not go back for mana after every gank. You should get this item ASAP. If you happen to find yourself with 1800 gold without having bought the previous items yet, you can buy the SoulStealer first. Do not aim to do this all the time though, go through the normal order for the regen and MS most of the time.
Finish your Sorceror Boots.
Lich Bane - This is your drill that will pierce the heavens. Start off with the Sheen. Once you build this your combo becomes even more devastating, and if your Buster Shot is on cooldown you will stil be able to put out some damage. Also it gives your rapid shot some meaning when it's activated to proc this.
Read on for what happens to your items after this point.
Start off with a Regrowth Pendant, and take the solo lane. I can't stress this enough, you need the solo lane to get to level 6 as soon as you can. You rely extremely heavily on your burst damage to do well and if your not higher level than everyone else then you will have a hard time playing well.
Level up your Rocket Jump first. Avoid using it to harass the enemy until you reach level 3 due to it's large relative mana cost at this level and low damage. Rely on your own auto attacks to harass the enemy.
Tristana's early game dominance starts from level 1 at the laning phase. A Tristana played well can be one of the strongest solo lane harassers. Don't be afraid to trade a couple of hits to keep the enemy champion at half hp, your pendant will keep you up and you want the enemy hero to be at around half hp.
Take Explosive Shot as your second spell at level 2, try to abstain from using it more than once every now and again since you want to keep your mana pool high for bursting him down later.
Once you reach Level 3, if you've harassed the enemy into oblivion his hp should be near the half way mark. Now you can use Rocket jump to damage them. If his hp is at 3-4 bars, then you can often kill them at this time.
Wait innocently at the creeps as if your just doing the standard last hitting but once he comes into range of your Rocket Jump then nuke him and hit him with your explosive shot.
If he doesn't Flash away after a couple of shots then finish him off with an Ignite. Even if he has Heal as his summoner spell this wont save him due to the anti-healing effect of explosive shot, and believe me I've had many of them use heal and rage when it had barely any effect.
If he does Flash away, or somehow manages to survive and escape, don't worry, he'll have to vacate the lane and go back to heal or he'll be low enough for you to rinse and repeat (and you should have enough mana).
Try not to spend too much mana on harassing, if your nearing level 6, make sure you have an almost full mana bar for your combo of Rocket Jump --> Explosive Shot --> Buster Shot.
If you add Ignite on to this, you will be able to kill almost any champion even if they're at 80% hp or so.
Once you reach level 6, harass them a bit to below about 600-700 hp and then nuke them to oblivion. If you managed to kill him, check the other lanes for the enemies' HP. If theyre in the 70% zone then your combo can kill them.
You won't have enough mana after unleashing your combo on your lane opponent yet though so farm a bit in the lane till your Buster Shot CD gets to about half way and then Recall back for mana and to shop.
If you've been doing well you'll have enough for your Philosopher's Stone and your boots.
I often carry around a couple of mana potions and health potions during this time to minimize the amount of times I need to go back to refuel.
Once your done shopping go gank the lanes. You should be able to get at least one kill every time from the massive damage your Rocket Jump --> Explosive shot --> Buster Shot combo can do. Don't forget to use and rely on Ignite everytime it's off cooldown. Return to farming mid lane once you've used it.
Rinse and repeat till the early game phase is over and they start grouping up.
Mid Game and End Game
This is where you start losing steam. Your still an unstoppable force 1v1 but the enemy team has started grouping up and it's harder to find situations where you can square off on a single enemy. Theres not much you can do other than wait till an enemy champion's hp goes down to about 70% and then pounce on them. If you've built your Lichbane then theres really noone that you can't kill one on one except for tanks, but they can't really kill you either if you just avoid fighting them. Even farmed Yi's and Ashes will avoid fighting you one on one since you can burst them into oblivion before they can even do anything.
Now comes the interesting part about this Tristana build. After you've built your Lich Bane you don't need anymore AP items, no one can survive your burst except for tanks and you'll really be much more useful as a Physical DPS.
Start building your Infinity Edge or if you want more slows and survivability, go for a Frozen Mallet instead.
The idea is to phase out your AP items as it reaches end game, once you fill out your remaining slots with physical DPS items, start selling your AP items starting with the Soul Stealer and buy the standard damage items such as the Black Cleaver and Phantom Dancer.
Although this build does alright on Summoner's Rift, on the 3v3 map Twisted Treeline AP Tristana is blatantly overpowered. The map is made for short games, small battles and early game ganking. You will dominate the game completely. Abuse it while you can, it's definitely not gonna last forever.
AP Tristana is one of the most fun characters on LoL and personally I'd like it if only I knew how strong she is, but sharing is caring. One last thing, as an AP Tristana even if you lose you'll have a hell of a time playing.