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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One trick for quickscoping is when you sprint, you get a little chevron looking crossheir at the middle of the screen. Use it to your advantage and put it on or near your target right before you stop sprinting and zoom in, and boom your sight's already on the person. I wouldn't suggest going into patrol and practicing on inanimate objects or even enemies, because the enemies are very mobile in this game, and most of the time you will not get the kill and inanimate objects of course don't have any aim assist so you can't adjust. Just keep practicing in control and stuff, hold down a choke point and hardscope. Don't forget to duck into cover if you miss. Once you get used to getting kills without having to fire a second time, you will start to see yourself getting quicker kills. Experience with other games like Cod also helps. Also, higher sensitivity, not lower. I run 8. Another trick is to just flank snipers with a shotgun, most of the time they don't see it because they are just zoomed in to one location. Or try not playing the lagfest called Destiny crucible.