This is Story Related and CANNOT be missed.
This achievement is unlocked after completing Level 3. Simply play through Level 3 following the in game prompts on where to go and what to do. During this mission you will have your first opportunity to choose a character to use during the “Dog Ambush”.
After you find Kevin you will be attacked by one of the dogs. You will have to choose which character to use. I don’t believe there is any difference in the character selection, so you can pick either. I have seen threads saying that the achievement for defending against 10 dog ambushes was not unlocking with Russell, so I stuck with Carl for most of the game. Follow the on screen prompts to defeat the dog and continue the level.