New Akali is fine, and let's not pretend the pre-VGU version wasn't hilariously broken even for an Assassin.
Put the healing on her passive empowered autos and give her old R back; A targeted dash that puts Akali behind the target, does a bunch of damage, and CD resets when she scores a takedown (remove the multiple charges because her Q and passive are a much larger part of her power budget now)
If I was working on her;
Passive, Assassin's Mark - Renamed Assassin's Pursuit
Deals ~~39-190(+60% bAD)(+50% AP) ~~ --> 35 - 150 damage (+50% tAD)(+45% AP) bonus magic damage and restores 10/15/20 10 / 20 / 30 energy
Now heals Akali for 10-60(+25% tAD)(+15% AP)
Q (Five Point Strike)
Energy cost 100/95/90/85/80 --> 60 / 55 / 50 / 45 / 40
W (Twilight Shroud)
Energy Cost: 40 / 30 / 20 / 10 / 0
REMOVED: Akali no longer restores energy on casting Twilight Shroud
NEW Effect: While in Twilight Shroud, Akali gains the bonus damage and healing from Assassin's Pursuit
R (Perfect Execution) Cooldown: 160/130/100 --> 60 / 40 / 20
Akali dashes in the targeted direction to a target enemy Champion, dealing 160 / 280 / 400 (+50% AD)(+60% AP) magic damage.
NEW Effect: Upon champion takedown, Perfect Execution's cooldown is refunded.