Akali isn't a champ until level 4-5, her energy cost is way too high to do anything and she just has to concede prio until she has enough levels so she can Q more than once. On top the matchup is free, she cannot contest the wave and her waveclear is dogshit whereas Irelia has top class wave control. In mid its a closer skill matchup because of the shorter lane, Akali with level can run you down if you over extend and then miss stuffs.

As Irelia, its just about hitting E and R inside Shroud, and that's 80% knowledge, once you've played enough against Akali (or even better if you do play Akali) you can predict how she wants to maneuver inside shroud and blind ult accordingly. If you can land the ult and get reset, you can set up the E reset, and Irelia wins the all in if she can get off the triple reset.