For the players going for this during their Hardcore playthrough, don't worry if any of the companions die on you, you will still get the achievement when you recruit the last companion.
House you can send your companions there when you dismiss them so you only have one spot to go to change them out. Also, it seems that if you are on good terms with Mr. If you're STILL having trouble unlocking the achievement keep each companion on your team for a good chunk of time, upwards of 5 minutes or so. I would recommend at least leaving the area where you recruit them before dismissing them. Make sure after you recruit them, you leave them on your team for a short while before dismissing them otherwise it may not register as them having become a companion. You can only have one of each type in your team at a time so if you want to recruit other companions you'll have to dismiss them first by talking to and parting ways with them. There are 8 companions in total, two robotic and six humanoid.
