This build is quite like most Akali builds only you can actually do things quicker with this build. I know I sound bias but I made this build a while ago and then finally tested it against the current top two Akali builds. With the top Akali build I failed miserably getting only one kill and died 8 times. With the second top rated build I did surprisingly better with 6 kills and 1 death. While using my build however I killed 26 enemy champions and died only once(mind you this was all against the new improved intermediate bots).
As you can see I have put down 7 items.
The last two items listed are interchangeable. For players who want to try a more tanky approach get the Spirit Visage. For players who want more damage get the Hextech Gunblade.
After you folow the item build for Trinity Force you should put the Spirit Visage or the Hextech Gunblade.
After After you have the boots, Trinity Force, and one of the items mentioned above you are free to get the other items listed in any order. However I find it more helpful if you get the Phantom Dancer as fast as you can, the extra movement speed and attack speed really help you stack up kills faster.
If you are not comfortable with Youmuu's Ghostblade you can switch it out for any item of your choice. I would suggest something that gives you similar attributes. If you think you can be comfortable getting kills with this try either Mejai's Soulstealer or Sword of the Occult. If you are unsure of how many kills or assists you may get try The Black Cleaver or Last Whisper.
The easiest way to farm is use your Crescent Slash Ability. It does excellent damage to all minions and heals you if you have taken damage from a recent fight. If you are alone in a lane and have minions you will be perfectly safe to push them on your own.
If you are losing a team fight it is always a good idea to use your Twilight Shroud ability to slow down the enemy team so you can regroup.
The best thing for you to do is try and hide yourself close to the enemy with out them knowing your there then jump in for a quick kill.
Move order in attacking an enemy
First you will want to get a surprise jump on them so you can give yourself enough time to cast all your moves in quick succession. First off start by hitting them with Mark of the Assassin then immediately use Shadow Dance and then hit them with your Crescent Slash. This is the most effective way to tons of damage in a very short amount of time. You may not kill them with one go around with all your skills if not just start from the beginning and do it all over again until they are dead. If the flash away or move quickly away from you then use you Shadow Dance to catch back up to them. If you want to throw Twilight Shroud in there and can use it to your advantage by all means do it.
Pros / Cons
Pros: Fully built Akali has great burst damage and can quickly move around the field ganking and slowing advances. If used properly Twilight Shroud can be an extremely useful ganking tool.
Cons: Early on Akali is quite squishy and can easily be countered and killed if your not careful. if you have to make frequent trips back to base you may want to get a couple more health potions until you get spell vamp and life steal. When seen people will usually target Akali first because of the danger she posses for her high burst damage.
Mark of the Assassin should be taken first as it will be your main damage dealer and first to get fully leveled up and it will give you some range on melee champions.
Twilight Shroud is taken next in order to give you the proper leveling up tree to get you all you damage skills in the right order and is leveled up last.
Crescent Slash is taken 4th so you can get more damage on Mark of the Assassin.
Your ult Shadow Dance will be taken at level 6, 11, and 16 like normal.
This is a fun build try it out and leave comments have fun.