This guide is for burst damage only. If played right you can deal a tremendous amount of damage whenever your first skill is usable. The important part of this build is to stay hidden whenever your first skill is on cooldown. In this way, if its done right, survivability items wont really be needed. The goal with this build is to be able to dive into a heap of champions, kill one on the way in, hide in the shroud until your first skill is up again and just show yourself when you have your first skill ready to deal crazy damage to the marked champion and then hide again. This is hard to master but when you do it will be deadly. I describe more of the playstyle under the items and tactics part of the guide.

Pros.

Great burst damage the whole game.

Very good ganker and chaser.

Great at surviving without survivability items if you master this strategy.

Awesome feeling to oneshot squishy champions with your combo.

Good at killing creeps in large numbers with your third skill.

Cons.

If your timing is off when you shadow dance in or if you are to slow to get your shroud up you can be stunned or silenced and that can lead to a painful death.

If you are up against opponents with Aoe spells that is targetable on the ground you have to be more careful in your shroud.

The runes and masteries is to activate Akali's passive at start and to give an extra offensive edge throughout the whole game. Also to give as much Magic penetration as possible since its one of the harder stats to aquire with items and one of the most damage boosting too. Still, the damage you deal with your ignite ap bonus and this setup is high even on lvl 1. This forces the enemies to be really carefull, if not, they will die.

I choose some items that i havent seen many use on Akali. Give it a shot, i think you'll like it ;)
These badboys is for me a must. As soon as i hit lvl 6 its off to gank. In this part of the game i only focus on ganking, and perhaps killing something in between the lanes if the timing for a gank is off. The thing that is most important is to get to different places fast and this item make it most efficient. Also, if that weren't enough, the best part of these shoes is that if you find yourself in a pickle, you can put up a twilight shroud and wait, stealthed, til the speed of the shoes is up again and then when the enemies are waiting for the shroud to end you take off in another direction at speed they cant match, if they dont have a range slow you almost always get away with that headstart. When people start to group up and go together i usually switch shoes to
The start of your most important source of damage. Early game this item is the best item for my Akali. The damage you get from 1 hit on a first skill marked target with your sheen is incredible at early game so this is when your mejas is gonna get thicker.
This item is for hunting guys down mid game. When you mark a target and shadow dance your way to him with your sheen up they will run after getting hit. If they dont run you just shroud yourself and only show your self to hit targets as soon as your mark is up. Eventually they will die or run. Either way is fine but in the second case, Rylais is a must. Before you can afford Rylais you can make up for it with the red buff.
This is the damage dealer of this build! This item will when the build is done oneshot squishy champions with your combo. After this point more ap is the only thing to go for.
is the best ap boost
There is no denying it, this item gives akali a very good boost. If you get hit jumping in or if your shroud ends this items lifesteal will hopefully make up for that even when fighting numerous opponents and if you get hurt somewhere on the map you just have to get into the jungle and do a combo on a creep and then you are fit for fight again.
is for ap too but first its to kill tanks, offtanks and people who have buffed up with magic resist if we have a ap heavy team. You will kill squishy heroes pretty easy but with Void Staff you will be able to handle those not so squishy heroes smoother. If its only the tank that has bought Magig Res items i usually getinstead. Together with sorcerer´s shoes this item will take care of almost all of a champions Magic Res for you and your team. A good way to be usefull even in the shroud.

This one is important since i dont go for survivability i need all the ways to get away that i can get. I try to jump in to sittuations where i can get out when all champions are killed or running but with flash i can get in to more dangerous sittuations and also avoid an ambush. Most importantly i use it for in and out kills like at a tower or amongst a heap of champions.
This one i use mainly to get the ap bonus that the masteries gives me. Those 10 ap makes a huge bonus damage at early levels plus later on you can use it to reduce healing on champions and kill of escaping ones or to counter Tryndas Undying Rage

You should ofcourse go for the spells that suits you the best but these are a must for me with Akali.

This is my first guide and if i have missed anything or if you see a weak spot that needs to be fixed then please comment ;)