In beginning of game play it safe and farm minions with your q ability. then when you get twilight shroud you can start being more aggressive. Try throwing it on the caster minions to force them out of exp range or you could throw it down throw a q and proc its effect for some harassment. Akali is pretty useless until you hit level 6. once u do if u are pushed back and the other person has low health throw down twilight shrow then throw a q ulti in to proc it thorw an e then repeat from the point when u threw your q until they die.
You can try some cool jukes to get away with twilight shroud and your ulti. With this build you should rape with her as long as you get fed early game.