Pros:

-Gets relatively tanky, while still doing massive damage
-Extremely mobile and fast around the map
-You're a flippin' Ninja

Cons:

-Lacks hard CC
-First clear kinda sucks
-Falls off late game
-Countered by hard cc/disengage

Tank Akali works because instead of focusing on burst damage and maxing Q, you max your E, Crescent Slash. It has an extremely low cooldown and is super spammable, while doing a sizeable amount of AOE damage. While Tank Akali does not have as much burst as an AP Akali would, you have much more survivability in fights, and you become much more useful to your team as a frontliner who can still dish out an extremely high amount of damage while also taking some as well.

The best mastery page for tank Akali is 12/0/18.

12 points in Ferocity really helps with your damage output, while 18 in Resolve gives you a key component of this build, being Grasp of the Undying. Grasp allows you to survive fights as you already have a large amount of spell vamp and lifesteal from your passive.

For runes I take 9 Hybrid Pen Reds, 9 Armor Yellows, 9 Magic Resist Blues, and 3 Movement Speed Quints.

Alternatively, you can take scaling magic resist blues, or scaling cdr if the enemy team has low magic damage.

As for quints, you can also take AP quints if you want a little bit of extra damage, but I prefer the movespeed as it helps with ganks and early map control.