Capture Maps on Overwatch are the following: Hanamura, Temple of Anubis, and Volskaya Industries. MUST be done on one of these 3 maps (at the time of writing this these are the only 3 maps for Capture at least).
In order to unlock this achievement, you must capture point "A", and then proceed to capture point "B" without dying. One thing to note is that you CAN die BEFORE capturing point "A", just not for the rest of the game after capturing it. This was tested and confirmed.
You must participate in the capturing of both points as well, from what I can tell, watching myself plus 2 other group members get this in a game.
Tips: Play whatever character you are comfortable with, but I highly recommend Roadhog. His self-healing, high hit points, and deadly chain grip does wonders for survivability. This is just what I was very good at using, but obviously every character in the game works for getting this achievement.
EDIT 7/6/16: It appears that using the character D.Va glitches the achievement, in that if the mech dies, but she herself does not die, it still counts as "dying" for purposes of this achievement. Many have reported this in the comments below.