My personal idea to get better aiming and the important 'situational awareness':
Just for training stay on passiv all the time and rely only on your vision, never stand still and wait, always move with at last half speed. When making a rest (max 10s) for orientation don't even move your torso -> every movement alerts the enemy and a camping mech is an easy prey for snipers.
Will take some time, but at some point you will 'feel' what is happening around you.
And
always have a teammate ahead of you, just to see what he is doing, what is happening.
...and to avoid to become a target yourself.

As soon you have found a target shoot it while already retreating until you are close to a new cover/dead angle.
For aiming: Practise to keep distance to your opponent and at least 2/3 of maximum weapon range should be your preferred firing range.
General tips for brawling (my favourite combat situation):
Move backwards as long the fight continues and do your circles -> moving backwards you will always have your enemy under your crosshair while he is speeding around you in circles thx to your damn tight turn. (even with a Bushy you will keep the upperhand against a nimble Scat)
Only with a fast light or medium (with masc) move forwards, use masc when you got the feeling his mainweapon has reloaded and he will shoot in the next 0.5s.
And 'X' is great as well for tight turns.
And never go full throttle in a brawling situation, 80-90% is enough to benefit from better cooling.
Edit: I'm totally with ~SJ~MausGMR (next post), surviving is more important than achieving kills.