Hmm glass cannon AP akali. I'm not totally sure about this. Looking at akali's AP ratios, they are nothing special, so building a **** ton of AP seems kinda weird. Also, with Shadow Dance, i'm sure that in team fights, you'll quite frequently be in the enemies' back line, or at least in their front line, which means that you will take a lot of AoE damage, or single target damage if your opponents are smart enough to buy pink wards.

I'd recomment building more tanky. Akali does a ton of damage with just her on hit effects, so i think it'd be better just to itemize more health to give you a larger window through which you can assassinate a carry.

Not going to upvote this guide yet since you haven't included anything about team fights, but PM when you do and i'll look at this again

thanks for your time,
-u