This is pretty straightforward. First of all, select the challenge of the same name for it to count.
Once the round starts, or whenever the two of you agree to split up, head in opposite directions and just keep going. Once Lara says something about staying in radio range, or she's going to "lose her" you're far enough. Just keep spreading out so you both have room to hunt for food and not accidentally get too close together. No matter what she says, neither of you will die from being apart at any range. Survive to the same point of time the next day and the achievement is yours.
This is also a decent time to work on "Sisters of Athena" and "For the Night is Dark" if both of you can handle yourselves against the soldiers. You'll get these twice as fast while split up.