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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Try high aim-assist snipers. Such as Her Benevolence, Ice Breaker, Prudence II, Eye of Sol and so forth. Also, on all snipers roll for Unflinching and Hidden Hand with the Ambush scope, Shortgaze or Longview. I snipe with a 5 Sensitivity and do very well.