Akali is an incredibly strong champion in the right situation. I've won team fights with her almost single-handedly. I also play Akali in mid lane, and I am also in Bronze (although I'll be in Silver in no time, at this rate). Here's my advice.
When to play Akali
• I don't suggest playing Akali against teams with hard crowd control (stuns, suppresses, silences).
• I don't suggest playing Akali when the enemy mid lane champion has a stun/silence/suppress in their kit (Malzahar, Kassadin, Cho'Gath).
• I highly recommend playing Akali when the enemy team is lacking in hard CC and the opposing mid laner is also lacking in hard CC (Lux is an exception; Akali owns Lux most of the time).
• Don't enter an all-in fight before you hit level 6 unless you are absolutely sure you can win.
• You are a melee champion, so you will get bullied by ranged casters.
• Akali is a difficult champion to farm with. Just do your best while avoiding excessive damage.
• You have no real escape, so be careful of ganks!
• Start out with either: 2 wards + 9 health potions or Long Sword + 2 health potions
• Final build should look like this: Sorcerer's Shoes, Rylai's Crystal Scepter, Liandry's Torment, Lich Bane, Will of the Ancients, Rabadon's Deathcap.
• Build Rylai's Crystal Scepter, Haunting Guide, and Hextech Revolver early in the game!
• Finishing your Deathcap should be the last purchase you make.
• At level 6, you should start harassing your lane opponent by diving in on them and dealing burst damage.
• If they stay in lane long enough for you to bring them to low health, tower dive them for the kill.
• If you win your lane, start roaming and getting kills/assists in bottom lane, top lane, and even the enemy jungle, if you are super fed and confident.
• Level up R whenever possible. Max Q first, then E. Level up W once at level 4 if you feel you need it. I find that I don't level up W until way late in the game, because I don't need it.
• I like this combo for bursting down an enemy: R, auto-attack, Q, auto-attack, E, auto-attack. (Those auto-attacks will give you tons of extra damage if you have Lich Bane. Even without Lich Bane your auto-attacks are strong because of your passive).
• As Akali, your job is to kill the carries (yes, both!) and then help your team finish off the rest of the team.
• I suggest killing whichever carry is the biggest threat first. If the ADC is fed, then dive in and kill the ADC in the first few seconds of the team fight.
• You can literally carry your team to victory by killing the enemy carries right at the start of a fight.
• You get stronger as the game progresses. Don't be too reckless early game; you aren't godlike yet, and you'll just end up feeding if you enter Rambo Mode too early.
• If you play well early game and get fed, you can practically 1v5. All you have to do is kill the carries, then deal with the rest of the team.
• If the enemy team has stuns, suppresses, or silences, you will get CCed and focused as soon as you dive. Let someone else (someone tanky) on your team initiate. Once they distract the enemy team, dive the carries.
• Your best friends are: Kayle, Amumu, Malphite, Sona, Hecarim. All of these champions work great with Akali.
I hope this helps! Enjoy!