As the title states, I use this build primarily for counter picking purposes.
Akali is good against (from lolcounter.com):
Karthus
Ezreal
Ahri
Nidalee

Akali is good with:
Diana
Shen
Katarina
Amumu

Akali is bad against:
Lee Sin, Garen (these guys are not worth getting counter picked by).

Jungle Akali does not work with AP items, she just doesn't. However AD Jungle Akali does work.
But, as the game progresses, the AP items allow Akali to snowball, and AD items do not.

So what is to be done? This was the problem I faced when attempting to re-invent Akali for the Jungle. This build will give you the added health, armor, and damage you need to be successful while jungling in the first 5 minutes (the most important for a Jungle Akali) of the game.

There are only two cons to a Jungle Akali:
The first being that she is somewhat vulnerable at start. The skill masteries, runes, and item build is designed to give Akali that early boost she needs to farm and clear the jungle quickly in the beginning, but not to handle deflecting a counter-jungler.
The second is that she can't really early gank, getting Shadow Dance is imperative for ganks, so don't expect to be picking up too many kills until level 6.

You will notice that in comparison to all other Akali builds, the Hextech Revolver is nowhere to be found here. This is because the bonus damage which Sheen provides from it's passive not only synergizes with her innate (Twin Disciplines - more spell vamp) but it also allows for greater burst when jungling and ganking.

In short, Sheen is the best option for a Jungle Akali after getting your Madred's.

What is also important to note is that the Bilgewater Cutlass is the other item opposite Hextech revolver in the recipe for Hextech Gunblade. So the trade is essentially an earlier damage and spell-vamp proc over early AP that isn't needed. You also get to use the slow from the Bilgewater Cutlass sooner than normal (assuming one favors going for gunblade after initially purchasing the revolver). This heightens your chances for more kills earlier on.

This is the real secret to success for jungling with Akali. The jungle route is as follows:
Golems > Red > Wraiths > Wolves > Blue. At start run straight to the bush opposite red and keep watch for any invaders trying to ambush.

At 1:25 run back to Golems and kill the small one first (spawns at 1:40). Be sure to use a pot when you begin fighting the Big one, and again when you are heading to Red (spawns at 1:55). Your health should never drop below half. try to farm up to 1100 gold as quickly as possible and head back when you have enough to finish madred's razors and pick up your boots.

From here you are ready to keep ripping through the jungle and get to level 6.

Your next items will be Sheen, followed by Mercury Treads, and then the Bildgewater Cutlass.

These 4 items are your early core, and the extent of which you will invest in AD items.
The Cutlass's active is to be used as much as possible; basically it acts like an exhaust with a 60second cool-down plus some nice damage (even better when you make Hextech). This active in conjunction with Shadow Dance and Twilight Shroud is amazing for ganking carries.

Early Core = Madred's Razors, Mercury Treads, Sheen, and Bildgewater Cutlass.

From here on out, you will be transitioning into your AP item build. You are now high enough level to where the advantages of AD wear off, and the need for AP centered items will dominate the rest of the game. Notice how each item (minus Madred's) can be built into AP.

First and foremost, you have to get Rylai's, followed by completing the Hextech Gunblade, and finally, converting Sheen into Lich Bane. I wouldn't recommend selling Madred's until you absolutely have to. I usually sell it when I'm completing the Lich Bane.

Mid Core = Mercury Treads, Rylai's Crystal Sceptor, Hextech Gunblade, and Lich Bane

With your Mid Core now solidified, you can now expand your killing ability with Rabadon's and Void Staff. These two items will bring a sizable difference to your damage output and spell vamp. Shredding carries will become boring and burst dps'ing tanks will be the new norm.

Late Core = Mercury Treads, Rylai's Crystal Sceptor, Hextech Gunblade, Lich Bane, Rabadon's Deathcap, and Void Staff

I must re-iterate that the first 5 minutes are the most crucial to success as a jungle Akali. If you are being counter-jungled, you may need a teammate's assistance to expel the opponent from your jungle (depending on what character is counter jungling you). If you can get through the first five minutes and your mid has ensured that blue hasn't been stolen, you are set to be right on track for mid and late game ownage!