Most of the time the answer's "You don't". You try to fight akali 1v1 at any point after 6 and you die unless she horribly failed lane.
Best case you can stalemate by being too damn beefy to kill, but she still has poke to wear you down with. Better case is she's bad and you end her multiple times until you have a considerable level advantage to shrug her off with. That's not to be relied upon.
Hexdrinker does help, if you're one of the heroes that can incorporate it into their build without being too far behind.