Close Call medals don't always register as they should, be here is a way to ensure that you will get them every time with a boosting method.
Player A - Getting the Achievement - Battle Rifle (Preferred)
Player B - Helping w/ the Achievement - Assault Rifle
Player B shoots Player A with the Assault Rifle with 3-4 bullets, then melees him. Player A then kills Player B as fast as possible, preferably melee + BR, while his shields are recharging. When they become full, the medal will come up. Repeat this one more time to gain the achievement.
If you are looking to get it legitimately, you'll just have to play and get a little lucky. I would suggest FFA over Team Slayer, as I think you are more likely to get these medals. Also, try to keep a 1 hit type of weapon on you, such as Rockets or Sniper, so that can quickly kill enemies after they take your shield and hit you 1-2 more times.