In this challenge room, you have to recuse the Little Sister from a Big Daddy that has gone crazy, but you'll have a limited selection of weapons to use. The only weapon that you'll find is the grenade launcher, and the plasmids that you have to work with are "Target Dummy" and "Winter Blast." You'll also need to find enough items to invent an Automatic Hacking Tool.
The video below will help you get both this achievement and "The 'I' in Team - Expert" achievement, which is for completing this challenge in under 3 minutes.
*This is not my video. Credit for the video goes to 0verlord73.