hello fellers this is my AP Tristana

an AP tristana can burst really good, and nuke someone, at the sametime though she's going into the enemy. So it's pretty much a suicide bombing tactic. you are an assassin and should kill your target in 1-2 seconds all while rocket jumping. and your main target should be squishies as some beefys can take your hit.

late game this build is useless but early-mid game your dominating 1 shot kills

i haven't tested it out yet but im pretty sure if you death grasp someone and then explosive shot + buster shot + ignite them you don't have to rocket jump to your death. although i haven't tested it

PROS:
Heavy Nuker
Can destroy most opponents in 1 second
Early game has a lot of burst damage without AP
This + Kayle's Ult = safe get away.

CONS:
Very vulnerable play style
Not as good late game
You will be targeted after nuking someone.
You do nothing after your nuke until cooldowns are up. (10 seconds)

heavy ap burst is what you want.

an ap nuker's wet dream

so what we want for a huge ap burst is just pure AP, trist's skills are too much on CDR. so she doesn't need any of that.
from here you can get banshee's veil or another nuke it's up to you

what i don't think you should get
you can't really proc the lich bane a lot and you don't need spell vamp because your a 1 hit burst.

and survivability for tristana could be useful although you do want to 1 shot people right?

ignite to finish em off

flash to get away (or chase? but you shouldn't chase if your nuke failed)

great passive, but not for our ap right now
cool but your ap
your bread and butter mixed with ur buster shot and explosive shot and ignite
who would live to that?
and when u kill someone it resets the cooldown
if only it was a single target nuke, but since it's a DoT it'll take a little while for someone to die, and a good side effect also so they can't recover
the ultimate destroying ultimate, it has a 1.5 AP ratio and has a good base damage.

AP trist, is my fun way of using trist. Not recommended for ranked play or anything but it's just for funs.