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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They use sniper rifles with high aim assist for distance killing on the move. For up close sniping, snapshot is a must for quick scoping. Easiest way to do that - zoom in with your scope and put a mark on your screen where the reticle is with a non-permanent marker. It's as easy as putting the mark on someone, scope in and pull the trigger before you're fully scoped, then let off the scope.