Start with this book and 1 hp pot to make ur spells deal more dmg

akali need spellwamp to keep her self alive and akalis passive gives her bonus magic dmg for every 20 AP she got

always good to get lover cooldowns on ur spells but absolutly on your Twilight Shroud spell without it ur like dead

1 of the most important thing in this build u will have 3 of them in the end the hextech gunblade gives you atk dmg ability power life steal, spell wamp and spellwamp but does not stack on each other but thats why you got your passive spell for every 20 ap u got u get 8% magic dmg and for every 10 atk dmg u got u get 8% spellwamp so this will be epic for both ur attack and spellwamp.
plus u can slow them and deal 300 magic dmg with the hextech gunblade just use it

akali is a low healthed char so u will need this and u get more ability power with it to and u will have a chance to slow them on attack and deal more dmg and ur cooldown will reduce by 3 sec

more ap is good for your dmg cuz with 3 hextech gunblade u will already have like 60% lifesteal and 60% spellwamp

Flash will be needed as escape spell

Ignite is good so they cant heal when low healthed and got a chance to kill them

this two runes is needed to make ur deal more dmg without spells in start and ur passive will give you some spellwamp at the start

this two runes will make ur magic dmg be mutch higher in the start will be needed