This is a story related achievement / quest.
This achievement is the end of the Old World Blues DLC and is simply your decision on what to do with the Think Tank after you have recovered your brain... or dealt with it.
There really isn't much to this achievement. It is the conclusion of the DLC and requires you to decide whether or not you wish to destroy the Think Tank or simply find another solution. Completion of Old World Blues will result in the completion of this achievement. Congratulations on finishing this fun packed DLC!