After defeating John Seed, liberating Holland Valley and rescuing Hudson from John's bunker, you will get a radio call from his wife saying that you two should come back to the house at Nick Rye & Son.
Once you get to the house you discover she is in labour and will require you to drive and drop her off at the Holland Valley clinic. This is a driving time trial side mission but the checkpoints are fairly forgiving. It is highly recommended to turn autodrive off for this one.
Once arriving at the clinic,
and the side mission is complete - you will unlock this achievement.
Edit: * This achievement appears to be glitched
. Many gamers have completed the quest without the achievement popping.
If this happens to you, check if the task is still in your journal after leaving the game and coming back. If it's still there, track the task and go back to the clinic.
The cutscene of the Rye's coming out of the clinic with the baby should play again and the achievement should pop.
If it doesn't, you may have to start a new game to try again.- Courtesy of TheUtmostLegend