The lights are on
What you need is at least one friend to play through the game with you. Start any campaign at the beginning with difficulty set to Easy. From here play through the campaign until you are in the safe room a the start of the last chapter.
At this point you will exit the game and you partner (who should be hosting) sends invites to all players who want the achievement. DO NOT ACCEPT THEM UNTIL TOLD TO!!! They will then play through the final chapter until the rescue vehicle is about to arrive (or you reach the resuce vehicle in Campaign 5's case). At this point the host should call a vote to change the difficulty to expert and position themselves near the rescue vehicle.
As soon as the vote passes the players that have invites should rejoin the game in time for everyone to get on the rescue vehicle. If this works properly you should be able to check your achievements stats and see that you have completed 1 (or more) campaigns on Expert.
Note: Campaign 5 presents a few challenges with the crossing of the bridge at the end. Therefore the host should ensure that they progress slowly but steadily across the bridge so as to maintain accountability and control of the other players.