At the start of Episode 4 with Claire, use the lever in the security room that controls the sluices during Barry's Episode 4. Successfully complete the rest of Claire's episode, then play and complete Barry's part. Afterwards, replay Claire's episode, but this time do not use the sluice lever. Complete Claire's episode, and then play Barry's episode, following the new path that is created, to unlock the "Routes Of Future Past" achievement after completing Barry's episode.