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.
My first build being published on this site, but I always use this build for her. It's never let me down once.
Start of with Amplifying Tome and potion. The added damage that Amplifying Tome gives her in the beginning of the game is essential for when you break the seal on Mark of the Assassin.
Mark of the Assassin is the first skill that you want to max out. Not only does the distance give you a huge advantage for killing off those champions with barely any life as they are running away, it works well with the Shadow dance for getting into range in order to break the seal.
I choose Boots of Swiftness over Boots of Mobility for one reason: It has a constant speed. Yes, Mobility gets you across the map faster, but when you are really in a bind and you get hit by a minion while running away, you are completely ****ed.
Mejai's Soulstealer is next, and let me tell you... if you are fed early on with Mejai's, consider yourself ready to just kill anything.
Guinsoo's is just ridiculous and is in every build for her so use it, it is a great item. Rylia's Scepter is an amazing item for two reasons: 1.)The health it gives you and 2.) The AP it gives you. Pair it together with Frozen Mallet and you'll be basically tanking in a way.
Hextech Gunblade I don't see a lot of people use, but I use it for her all the time. The abilites are amazing and it works with both damage and AP.
Put all this together and I truly believe you will have a successful build with Akali.