Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
I noticed how Akali is somewhat weak but with this build I have found her to be a tough opponent. With the skill masteries and runes you start off with some life and dodge to help you stay in your lane for a good portion of the game. The two damage runes along with Doran's Blade triggers your spell vamp passive from the beginning so you can get your life back from fighting a few waves if you get harassed. The trick is to not let the other team harass you at all and keep using your Twilight Shroud to scare them back and take control of the bushes. If you don't need life then do not attack the creeps, just get last hits and focus on attacking the enemy to keep control.
When you die or need to go back pick up boots and amplifying tone, upgrade the amplifying tone to Mejai's Soulstealer if you doing good in your lane or go straight to Hextech Revolver if you are having some trouble in your lane. Get boots after that if you are able to, I pick different boots depending on the team I am playing against but for the most part I like the dodge that comes with the Ninja Tabi boots. Sometimes I get Sorcerer's Shoes if I am doing good and able to get Mejai's Soulstealer.
When you head back to your lane you want to keep yourself busy and trying and rack up as much experience and gold as you can. It is going to be hard to destroy the turret with Akali early game so just make sure you at least have lane control then go jungle or gank to keep building your champion stronger. Akali is good at tower diving, especially with the dodge that she has, so don't be afraid to go in if the time seems right.
Once you have your boots and Hextech Revolver, start working toward either Hextech Gunblade and/or Lich Bane. I get sheen after Hextech Revolver. After that start building for Rabadon's Hat if you have the money or Will of the Ancients for almost 90% spell vamp endgame. This Ability power with your spell vamp will give you the ability to retrieve all of your life back very fast.
Keep in mind that you didn't get any life items so when you are in a fight you must commit and keep doing spell damage to keep your life up. If you are really having trouble doing this then you might want to get Rylai's Crystal Scepter or more life steal, preferably starks for the armor pen and attack speed if you go life steal. The focus in this build is to rack up ability power so try keep up with that if you can.
Good Luck :]