As you see, akali is like an hybrid champion, but more for AP. Her passive, will up your spell vamp with AD, so you must buy a good quantity of it. For more resistance in a fight, her spell vamp have to be in a good percentage. The combination of Hextech Gunblade + Will of The Ancients can generate 40% Spell Vamp, plus her passive bonus, you will get high health while damaging. Frozen mallet and Rylai's Crystal Scepter might help you chasing champions and fleeing them. Be care while changing this build, because you can get bad defenses or damage. With difficulties for killing tanks, get a Void Staff.

Akali Can Deal TONS OF DAMAGE in a single rush, Try Marking the target with her Q than jump with her ultimate, then use her E, activating the mark. Akali is a nice assassin but is a little bad in team fights. She cannot deal too much damage to much targets her E range is not so good at all. Her ultimate range is really nice, use it to jump in ranged or support champions, that can die easilly. To lane with her, try taking enemy's life with Mark of The Assassin, while in the correct time, kill them. Remember: Care with ranged champions while you dont have your ultimate. And, while getting Shadow Dance first time in a game, wait getting some more charges, or it'll be inutile. Akali is more a Late Game Champion.