Welcome to my guide of the hybrid Akali.
This is my most important tip for her;
this unit is a flipped ninja PLAY HER LIKE A FLIPPED NINJA!
P.S. listen to her joke (/j) it is realy funny

Runes and Masteries are realy important for Akali. You need to use your runes and masteries and your starting item to trigger your passive. In my build you start with Amplifying Tome so you already have enough AP, now you only need AD. Pick all AD carry offens masteries, finish your masteries with some AP carry masteries. Take Greater Mark of Attack Damage and Greater Quintessence of Attack Damage to completly trigger your passive. Also pick some tanky runes, just to survive longer.

You can also choose to start with a Long Sword and pick more Ap runes and masteries, but i think the other chois is better.

Akali is a hybrid so you need to get hybrid items. Rushing Hextech Revolver gives some nice spell vamp and Ap. I'll talk about boots down below, just get Boots after your starting item, and full build you boots after Hextech Revolver. Pick Hextech Gunblade, now you are realy hybrid, you have nice Ad and Ap and lots of health back when attacking. But you die to fast and many people still escape, you need to be more tanky. you need to get this to items

1. Rylai's Crystal Scepter
2. Frozen Mallet

they give you some nice CC and you get a strong tank, now you can buy your last damage. Pick Guinsoo's Rageblade and Trinity Force and your build is finished.

boots

Boots is hard to choose for akali, there are five things you can pick


Sorcerer's Shoes is for full Ap, you are not so I shouldn't pick these.
Mercury's Treads is strong against Ap, and gives tenacity I realy like that and I should choose these.
Ninja Tabi gives armor, pick this against a carry mid like Ezreal or Urgot.
Berserker's Greaves is for full Ad, you are not so I shouldn't pick these.
Ionian Boots of Lucidity gives cooldown, this can be nice, also a good choise.

Open with Mark of the Assassin its great to spam, or farm minions out of your range, also max this abilitie first but, your second abilitie Crescent Slash also is great to farm and deals some nice damage, it can also trigger the mark of Mark of the Assassin. Get one point in Twilight Shroud, its just for the slow and your invisibility. Your ult Shadow Dance needs to be maxed in lvl 6, 11 and 16 it deals nice damage and people can't escape you easy.

Flash, use this to be tricky get in Twilight Shroud and flash away, it's an easy way to escape.
Ignite, deals the last extra damage you need.

other good choises
Exhaust, gives you some extra CC.
Heal, with just a little more health you can fight someone easier with you spell vamp and life steal.

bad choises
Clarity, if you think of this, uninstall game and never play LOL again.
Clairvoyance, is for support.
Smite, is for jungler.

Your extreme deadly combo can be done in lvl 6, before lvl 6 just safe play and only farm.

q -> e -> r -> 2x basic attack -> r -> q -> basic attack -> r -> basic attack -> q

I know this is an extreme big combo but it's just easy, use q whenever you can and trigger the mark, use r if champs get out of range, use basic attack when your spells are on cooldown. Also use your Twilight Shroud for extra CC.