Personally I think there's 3 major changes that need to be made.
Her passive needs a rework, the passive they gave her will always be garbage at least with its current order of operations and I doubt Riot will just give Akali the damage on first strike because it would give her access to immediate burst. The simple fact is that most of the time on your first hit you're at or near full HP and the heal just goes to waste.
What I'd do is make the passive 'After hitting an enemy champ with a basic (non-ult) spell your next AA deals bonus damage and after hitting an enemy champ with an AA your next spell has spell vamp. This effect is doubled if the passive has not been proced in the last 4 seconds.' Give Akali the choice between fighting and repeated passive procs or more powerful, lower risk but lower overall reward procs.
Her R needs to have a lower CD as you rank it. 2 seconds is just too long late game. Either 2/1.5/1 or 2/1.75/1.5 would probably be fine, just not 2 all ranks.
Finally her W needs to be reverted. This spell was just better before the rework and very few Akali players would argue otherwise.