Give this weapon another chance. Seriously. This weapon gets no love at all. You could argue that the .44 Revolver from Fallen Nation is a superior weapon, thanks to its higher one-shot kill potential and much better damage at range than the Mamba, but please. Fallen Nation's servers are so haywire that you can't try that weapon anymore. It isn't too late to try and love and have a blast with the Mamba.
Here is my load out with the Mamba:
Secondary: Black Mamba w/ JHP rounds. Never equip Wadcutter rounds or Explosive rounds. They severely reduce the Mamba's one-hit kill potential, which is arguably the weapon's strongest selling point. JHP rounds will enable you to kill even Paragon Juggernaut foes with one hit.
The grenade is up to you.
So, the best way to use this weapon is like the way you would quickscoping with the X6 .338, albeit without the magnification and low mobility and infinite range. If you are half-decent at quickscoping, you should be decent with the Mamba. Aiming down sights will guarantee you a one-hit kill within relatively close range.
The hip fire box with the Mamba is relatively minuscule, so when you feel like an enemy is about to go into your crosshairs, tap the aim button and fire. Just be sure that you aim for the upper body, as anything below the lower stomach will result in a two-hit kill. That is the procedure that you do over and over again, especially has hardscoping with the Mamba is very ineffective in my experience, thanks to the misaligned and obtrusive iron sights.
Be sure to know when to engage the enemy and when not to. If the enemy is too far away, don't even bother engaging, not unless they are turned away. If they start firing at you, use the high mobility of the weapon to get behind cover. Only use this weapon in close-quarters, where it will dominate everything else along with sniper rifles, other Mamba users, and shotguns. This is my secondary of choice for my sniper load out on MC4.
You can pull off the occasional mid-long range shot on an unsuspected enemy, but this type of firefight should be kept to a minimum.
If a teammate has nicked the enemy just once, I recommend you just hip fire, as you will still get the one-hit kill.
SUMMARY: Only use this weapon in close-quarters combat. I recommend that you use your movement to aim, not actually swiping your screen to aim. Know when to engage and when to back off. When you encounter an enemy in close quarters, when your crosshair is over the upper body of the enemy, aim and fire. You will get a one-hit kill easily.