Although the Dog Tags are reasonably easy to find throughout the campaign and wouldn't require much searching (you come across most of them travelling from one objective to another) I found that the easiest/quickest way to do this was to repeatedly replay Chapter 1 - Mission 2 until the achievement unlocked.
There are 3 Dog Tags in the mission, you can't miss them and the mission only takes about 90 seconds.
While doing this reasonably short grind, can also work towards:
Grenadier - 5G
Kill the enemies with grenades
MOBA Master - 5G
Destroying the tower is mandatory for the main objective
Medal Of Honor - 5G
Unlocks through natural progression.