When I first saw the description for this achievement I thought "ok, just take your time & don't panic". It turn's out that this is so much easier than first anticipated. During the second level of the DLC, you will go to the Sulaco's weapon control room. When you sit in the gun control chair you'll view the targeting screen & a red X will be "painted" over the target area of the umbilical. The painted x will wobble around slightly, but just aim your crosshair over the general area, hold the RT button & release to fire when the weapon is fully charged. Do this a total of four times to unlock an easy 20G.
BrumtownMangler mention's that he first tried this on the Ultimate Badass difficulty & it did not unlock, but did when he tried again on recruit. Therefore there could be some kind of glitch on the harder setting.
Ok it seem's that other's are having no difficulty at gaining this on the Ultimate Badass difficulty, the only other tip I could mention is be patient when firing the 4th shot. The red x will start in one position, move up, then to the right before settling on the umbilical.