You must kill Dalton in under 40 seconds. Easiest done on recruit in co-op.
Once the fight with Dalton starts have both ppl use PMK's or if you can't shoot well enough with it then use AK-47's. You must knock him off the bridge within 10-12 seconds max, if you have to reload or if he walks too far to the right, it has taken you to long. Once you do this and he is knocked off, immediatley after the cutscene take out your sniper, use the M107, and have both people instantly start firing headshots at Dalton, he should be across the room, once the cutscene is done he will directly across the room from you. It might help to take 2-3 steps to the left to get a clearer shot. If you both hit him with 2-3 headshots you should make it in under 40 seconds. The achievement should pop up about 2 seconds after he dies so you will know.
Now this is a very difficult achievement, you won't get it quickly. you and a partner will have to practice this many times. The most key part is being able to knock Dalton off the catwalk in about 10 seconds, 12 max!! Try to get him before he goes past the first bend of the catwalk. Just open fire right away with a PMK or Ak-47, me and my friend used Ak-47's but PMK does more damage but is less accurate. To get the headshots you will need to get lucky. Sometimes Dalton will run and hide, but right when the cutscene ends you will have a few seconds where he is out in the open shooting at you and if you get lucky he might even stop to reload before running to cover. You have to have your hand on the LB button in the cutscene getting ready to swtich to sniper. Once that scene ends run 2-3 steps to the left if you need to and instantly line up a few headshots. Like I said I got about 3 off on him and my friend got about 2-3. The headshots are key.