Surprised there is not a guide to this, because you can mess it up. The biggest key to getting this is to not play multiplayer (online or "couch" co-op) using characters you haven't unlocked yet. If you do, then the companions will not appear when they should in the story, and you won't get this achievement without going back to a prior save or restarting the campaign.
Also, there is a side quest that you must pursue to get the third companion.
The order the companions appear is based on which particular main character you chose at the beginning of the campaign:
(1) Lucas: Anjali (will appear in a cage in cave after a mini-boss), Katarina (will appear on a bridge shortly after killing the first boss), Reinhart (in Stonebridge, during the Krug side quest)
(2) Anjali: Lucas (will appear in a cage in cave after a mini-boss) , Katarina (will appear on a bridge shortly after killing the first boss), Reinhart (in Stonebridge, during the Krug side quest)
(3) Reinhart: Anjali (will appear in a cage in cave after a mini-boss), Katarina (will appear on a bridge shortly after killing the first boss), Lucas (in Stonebridge, during the Krug side quest)
(4) Katarina: Anjali (will appear in a cage in cave after a mini-boss), Lucas (will appear on a bridge shortly after killing the first boss), Reinhart (in Stonebridge, during the Krug side quest)
The first two companions you acquire are very hard or impossible to miss (again if you are playing solo). To get the third companion, when you are in Stonebridge, get all of the quests from the Meisters. One of them will be to deal with the Krug in the prison in the same building; do this quick quest and the third companion will appear.
You will get this achievement after getting your last party member. If you have doubt whether you have messed this up, beat some monsters and look at the equipment that you pick up. If you get equipment for a companion before the key points in the story described above, the companion's portrait on the equipment should be blank. If you can see a portrait before you legitimately acquire the companion, you need to go back to an earlier save or restart from the beginning to get this achievement.
Edit: This achievement may still glitch on you, even if you don't play co-op. It really isn't known why. If you go all the above and the third character still does not appear, try and then play co-op and do the Krug quest to see if the third character appears. This happened to GameTagwastaken, and he was playing as Reinhart. One safer bet probably is to play as only Lucas until you get this achievement.
Please comment if you have any more information.