Cerberus Turrets are one of my least favorite enemies in the game (followed closely by Banshees) for exactly this reason.
First, if you're an Infiltrator, dump one point in Sabotage early on. It's all you need to convince the Turrets to turn on Cerberus. And boy does that feel good.
Second, if you know you're going up against Cerberus, bring along EDI. She's got a couple of useful abilities. Firstly, she has both Overload and Incinerate, which, when properly ranked, can fully eliminate one of the turret's two defenses, leaving the other for yourself or your second squadmate (like, say, Garrus). Secondly, Decoy is quite good at absorbing and attracting fire. Decoy is even available as a bonus power if you're so inclined, and will happily soak up turret after turret for you.
Third, learn the turret's firing patterns. It is utterly lethal when it's spraying lead at you, but after a barrage, it spins down and stops for a second or two. That's your cue to pop out of cover and let fly with your abilities, accurate weapon fire, and so forth.
Finally, if all else fails, see if you can avoid it. Turrets don't count as enemies whenever you have to defeat waves of enemies - you kill everything else, if you can run by it, you're golden.
And, trust my personal experience when I say, never ever biotic charge a turret while it's firing. It won't end well.