Akshan should be played as a hybrid assassin/ADC mid laner with the ability to situationally switch between burst damage and ranged poke depending on the current game being played.

Because there are so many things that can block the R shots like enemy champions, minions, and turrets, you'll find your ult gets blocked most of the time. To counter this you can E swing or flash to find another angle or better yet, only use it cleaning up a fight in an open area.

Level 1 use your E to swing onto enemy applying passive + PTA and auto as they run away. This should do 60% of their health and out trade allowing you to have early prio in lane. You should hit level 2 first because of your prio and use auto + Q to apply passive.

Your wave clear is not good until you get some attack speed and Kraken so your only hope to win lane is to engage enemy mid laner and force them out allowing you to push wave and roam.

Play the rest of the laning phase as an assassin, pushing wave and looking to fight with jungler or gank lanes with W stealth.

You can either play for picks using W stealth and E damage or play safe and use your kiting capabilities. Either way the possibilities of carrying the game are extreme because of the Revive.

It is always worth to dive the low health scoundrel to revive 2 or more teammates or the jungler if you think there's a chance your team can contest objectives.