I need help from AP Eve players
AP Eve doesn't feel strong. I can't 1v1 high priority enemies or even kill them fast enough playing AP. Playing AD or Off-Tank AD I can but AP Eve doesn't feel Strong enough because while with AD I can use my Q, E, E attack speed buff,R and Auto Attacks, With AP I feel I can only use Q E and R.
Just to be clear I'm talking lane Eve, top, rarely mid. Jungle advice could probably still help unless you're relying on smite for combo damage.
These are some of the build's I've tried out:
+3 other items
+3 other items
I've been trying to recommended build's suggestion of
first>
second. If my team feeds heavily, by the time I get
I can't deal enough damage with Q to matter. If I rush
I'm too squishy to stick around long enough to get the kill. I've tried
into
but I notice I can't 1v1 anyone that has lifesteal. Pretty much playing a Mundo-like damage sponge at that point.
What AP build gives Eve a good amount of burst? Do I just have to buy all the [Spell Effect] items like:

because I feel like any mage could do that and it's not something that specifically synergizes with Eve but if there's nothing else then I don't know.
Also what playstyle do you use when playing AP Eve? like aggressive, poking, defensive, mainly ganking squishies, etc.

because its cheap and gives you another nuke to use to BURST. From there get
Boots of your choice (Sorcs Swifties or Mobi's) and a last item for specific situations (GA Mejais Zhonyas Etc..)