How to prevent the chicken breasts from drying out
The reason why your meat is dry has less to do with whether you cook in liquid and more to do with the temperature you cook the meat to. The proteins in meat will squeeze out the water in them as you increase the temperature you cook them at. If you are cooking your breasts in boiling water then that can result in meat that is cooked far above well done. Here is a link that relates moisture loss in meat vs cooking temp:

http://www.seriouseats.com/2010/03/how-to-sous-vide-steak.html

This link is for beef but the basic principle applies to chicken as well.

Water is able to transfer heat much more efficiently then air given a similar temperature. This means that your chicken is ironically getting overcooked because of the water you added. A standard technique people use to cook small cuts of meat is to brown both sides at a high temperature and then lower the temp to cook the inside without over cooking the outside. Next time just try to cook without water and just lower the temp instead. Flip the meat often to ensure even cooking.

If you want truly "melt in your mouth" chicken you will need something with a bit more fat. Chicken breast is very lean protein and at best can be "juicy" but that is it. Chicken legs and thighs however are higher in fat content and have collagen which can result in very tender chicken. The legs and thighs can also be cooked to a much higher temperature without drying out as much as chicken breast. Consider cooking dark meat for tender chicken.