What's the best way to deal with Terror Missions early on? The laser turrets on the terror ships shrug off basically everything I've got and Personal Armor isn't enough to survive its return fire. I've tried using Tritanium Shrapnel Missiles and EMP Grenades, but even those usually don't do enough damage to destroy a turret before it kills off half my squad.
No armor will be able to withstand the fire from laser turrets; like sectopods, they have base damage of 200 (with 0-200 % range). They have night vision of 20, but no thermal vision. They are sniper units so having been spotted by an enemy unit will mean it will fire on you even without sight if there is a line of fire.
So in order to survive, you will need to use cover, work from sufficiently far away and/or not be spotted by any units.
EMP is not all that effective against them. But shrapnel charges and missiles are, primarily because their gold shield with 200 capacity is bad against cutting damage. It is strange that you have had problems with this.
I think shrapnels have always done the trick for me. A tritanium shrapnel rocket might even take out two with one hit, when they are close to each other. I think for you the main issue is how you get to fire at the turret, preferably in a manner that you won't get spotted by the enemies or can get into cover.
You don't actually need to deal with any terror ships at all if you don't want to. There is one mandatory end-game UFO which also has these which you will need to deal with. So a bit of practice could be useful at some point.
