This is a story-based achievement and can not be missed. It happens toward the end of your initial battle on earth, which also serves as the game's tutorial.
Just before leaving Earth, Shepard hops onto the Normandy and waits for Admiral Anderson to join him. Anderson says he won't go, and tosses Shepard his dog tags, reinstating him as a member of the Alliance Navy. The achievement should pop either as soon as this happens, or directly after the cutscene, I've heard people say they experienced both.