If I want to beat Akali I like to take Swain in mid, and I like to take Jayce top.
Primarily because they both have great counter initiation methods.
Quick guide for Swain: At early levels (1-3) use your range to you advantage. Harass with auto attacks and E. Levels 4-5 only harass with E unless your full combo will kill her. Only use Nevermove if she goes in on you. At level 6, use skills as you deem necessary, ONLY engage her when you are among enemy minions. From this point on, you are more useful than Akali.
For Jayce, just punt her around a bunch every time she goes in on you. use your range early game.