A near death experience occurs when you are shot and your HUD turns dark yellow with blood stains around the edges. Once this happens, just take cover as soon as possible or kill the enemy shooting you to allow time to replenish your health. You must do this a total of 5 times without dying in a row. If you play the game normally on hard and take your time, making sure not to die, you are likely to get it without specifically trying for it. Also, you can make yourself seen to an enemy until they shoot you, and then prone behind cover until you get full health back, and repeat that process 5+ times, until the achievement unlocks.