The best and easiest way to unlock this achievement is to play each map in private. Start a match of Adam Grab on the following maps and capture the Little Sister. Then go into a public match with your boosting partners and take turns winning.
Have one person pick up the little sister for a few seconds and then set her down. Repeat across 4 rounds until everybody has the achievement.
NOTE: Do not quit out of the multiplayer aspect of the game. If you do, you will have to re-do all that work over again. You can quit out of the map and still get the achievement if it's not a DLC map that the game gives you.