Akali is a very fun champion who can deal tons of damage very quickly and can stop somebody from escaping with ease (if they live that long) and on top of that she has a stealth.

Pro's

Can go into any lane
Amazing damage output
Decent surviverability
Deceptively strong
Great chaser
Can jungle
Very fun to play

Con's

Squishy in team fights
CC will can cause you major problems
Oracle's can stop you escaping
Requires skill

Magic pen marks so you can keep that damage up all game
Dodge seals so you can actually kill their DPS
CDR glyphs because she dosent need mana so only cooldowns cause problems
AP quints because that will trigger your passive at lvl 1

Start of with dorans blade as this will trigger your passive at lvl 1. Next get a sword of occult and go for those easy kills. Then get Mercury treads to counter CC. Then get mejais because the Ap and CDR from it mke you extremely strong. Next get a ryli's because the HP and ap are nice but the slow is best because your ulti will slow them so the definately can run (unless its master yi with his ulti up). Next get a hextec revolver becauuse its an amazing item on akali and gives spell vamp, lifesteal and AD and AP if used with her passive you will do alot of damage and have around 40% spell vamp. next i get a rabadons for the 155 ap and 30% increase. with full satck you will have around 260 AD and 720 AP and about a 2 sec CD on your Q however ive only gotten this far once.

9/21/0 because you need surviverability and the magic pen on offence. this is really down to preference.

Max your Q first because its the main source of damage getting a point in your stealth at lvl 2. this is down to preference but always use your stealth and max it last.

Akali is extremely strong and fun to play. You will rape anybody you want. Squichies are your main target beacuse the simple combo should kill them before they know what happened.