I consider myself a decent sniper, but when I go into Crucible, I'm wrecked beyond belief. There are guys who headshot me the very second they scope in. It's -blam!-ing ridiculous! I don't understand how they do it!
EDIT: A lot of people are saying that they get their skill from Halo. However, I actually snipe very well in Halo, but not-so-well in Destiny.
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I don't know about the rest of the snipers out there, but I find that primarily using my left joystick and strafing over trying to use my right joystick creates better outcome. Not only does it have the potential to dodge the incoming sniper shot, but if you set the scope at head height and just strafe, you rarely miss and hit them in the body. Obviously this does take some more room to move around and it is not as conducive to sitting in one spot without moving.