The best way to win is to Keep moving

The game is won and lost by obtaining some kind of advantage. Paintball strategies that incorporate lot of movement usually have the advantage. In paintball the advantage is in movement (usually). When all else fails, shoot and move to gain an better position. Keep you opponent from viewing your next move by shooting at their position a few times, then move quickly to your next position. A better advantage is where you move to a position that gives you a better angle on your opponent without him or here seeing you get there.
Staying in one position increases your chance of getting eliminated. It does not increase your chances getting more eliminations.
If you don't get an angle on your opponent, move to a better position. And if you don't eliminate your opponent after a few attempts, move.
If you get to a better position, don't give your position away by immediately standing up and shooting like crazy. This will give your position away. Take a peak to see what your battle field looks like. There may be a few targets, or there may be an even better position (or bunker) in your grasp.