You don’t have to do anything in your lane against Akali as Nasus. She has to stop you from getting stacks, or else you can just start pushing the wave and threatening to stack-check her under the turret.
Prioritize your rush item, Trinity Force, over defense unless you need it because you are losing. Even when you buy defense, buy only what you need. A Null-Magic Mantle if she’s a little ahead, Mercury’s Treads if somewhat, and a Spectre’s Cowl if she’s fed.
If you survive lane and don’t lose much of your farm or Turret health, then Akali must make plays during the mid-game, where Nasus is strongest. Finish Trinity Force and then just run at her or the bottom Turret with deep wards in the enemy jungle.