Drop your sensitivity down until you get better at reacting and aiming/shooting. Practice on the easier enemies to kill. Aim for the weak spots always.
Once you're good at sensitivity 1/2, try 3/4 and see if you can still keep up. I think 4 is an ideal sensitivity to play Destiny on, fast enough to turn on nikkas in Crucible, slow enough to handle any mobs in PVE. Sensitivity is mostly for you to find a level of comfort with aiming and movement. Find what works for you, although I will say in PVP you'll want to be able to turn around quick, so a 1 or 2 sensitivity might disadvantage you.
Obviously take cover when getting shot, crouching takes you off radar. Play smart. If you can't aim well then try and use your positioning to give yourself an advantage. It's always easier to shoot down on an enemy from a roof than it is to shoot at an enemy on higher ground. Positioning is the most important aspect of shooters IMO. If you just stand in the middle of shyt you're gonna die. Try and post up around places with a few spots for cover.
Melee everybody close to you, especially if your clip runs out. Get into the habit of melee'ing after you hit someone with your shotty for an almost always automatic kill. Use grenades to flush out enemies in cover, or help clear those waiting around corners. Don't chase in PVP because nikkas will wait for you around the corner with that shotty ready to ring off.
Also experiment with scopes on weapons that have upgrades. Sometimes people enjoy iron sights, others prefer more traditional holographic scopes. Aiming down sight is a big part of medium to long range shooting, so having a good scope is always advantageous. Don't zoom in unless you've found your target, you'll just be covering up your radar which is your best friend, plus your sensitivity in scope is usually slower..
End of the day though, just practice and find what kind of weapons you're better with. I'm an aggressive player so I like guns that hit hard or fast. Shotguns and AR's. On bigger maps, I'll run Pulse rifles and Sniper for range, but you want to ensure you can defend yourself in all types of battles(close quarters, mid, long range). Keep playing and you'll eventually pick up general shooter knowledge through opponents.
