Your Win Condition
You need to get an early game advantage before she reaches level six, because after that point, she can potentially kill you whenever she wants. Winning early often means rushing Hexdrinker.
General Strategy
I suggest running Doran's Shield due to her poke potential, alongside Ghost and Flash. Rush Hexdrinker as your first item, especially if she has Ignite and Conqueror, or you will struggle significantly at level six. If you manage to get a massive solo kill early, you might be able to skip Hexdrinker. Your full build should generally be Hexdrinker into Stridebreaker, unless the enemy team has an AP jungler, in which case a full Maw of Malmortius might be better.
Trading Patterns
Akali wants short trades; you need extended trades. Aim for a big level one all-in. After she hits level six, if you do not have Hexdrinker, you must play very respectfully, farming from a distance with Q and ensuring she cannot just Q, auto, and all-in you. The time between her leveling up and your purchasing Hexdrinker is the most dangerous window.
Wave Management
Your priority is to get priority no matter what. Crash wave two decisively, potentially into a proxy, and then wave three. Hitting the wave a lot is beneficial because the wave sustains you against her poke since she is energy limited. If an all-in isn't available, stack waves four and five to crash them together for a clean recall, ensuring you are strong for the next all-in timer (level four or five).
Their Win Condition
Akali wins by using short trades. Her main threat is hitting level six and having her ultimate ability, allowing her to burst you down, especially if she has Ignite/Conqueror and you don't have Hexdrinker.
