Pros -
-Her shroud gives her an Array of pros. You can utilize to intimidate and instil fear in your enemies psychologically. You can use it to slow enemies that are chasing you or chasing your allies. You can lay it down over a bush or wall to see your enemies location. You can use it to escape if you place it correctly, with her ult you can place it over a wall where a neutral monster is and fly over to it. You can use it in chasing enemies for it slows them.
-If you have the right runes and masteries she has INSANE base stats with her passives. You can utilize it to get early kills and getting some Kill Secures.
-With her high sustain with spell vamp and life steal and hybrid AD/AP builds you can basically go 1 vs 1 against any champion. She is just that powerful. If you are fed there is pretty much nothing stopping you.

Cons
-She is really squishy early on so make sure you get early kills and get fed first or else it will be a Long Game.
-There are a number of champs that counter Akali; Darius, Fiora, Jax, Diana, Renekton, Pantheon, Dr. Mundo. Renekton in my opinion is the hardest to fight against. But even these champs will have a hard time 1 vs 1. and if your fed it won't be hard going against them.
-She just does not have many cons. Honestly she might be the best champion in the game.

Make sure you let your teammates know that with you being Akali that Kill Secures and Kill steals will be inevitable. Akali is the Athena of stealing kills, cs, wins, experience points and just anything that can be stolen. Akali really isn't a team player. What you want to do is get as many kills as possible and later on when your fed try to get the enemy low and let your ADC or top/mid get some, because ultimately to win, your team has to be fed. She works well with just about every champion, usually champions with a lot of AEO synergize with her great so she can come in deal finishing blows. I personally have an 84% winning percentage playing as Akali, She just doesn't lose games. I have 189 wins and 189 losses so I am the epitomy of the Average player lol, so for me having an 84% WP with Akali, it has to account for something.