Make sure to get a Jetpack and keep it until the end of the mission. After you fly in the Falcon and land on the beach, go left along the shore until you reach the cliffs at the far end.
A user below states you can simply start from rally point Charlie.
Avoid the two Wraiths or destroy them if you wish. You can activate the missile battery nearest to the far end of the beach for a checkpoint before attempting this.
At the far end of the beach, jetpack up over where the cliffs meet the water and keep jetpacking forward until the 10-second kill timer goes away. From here, just hug the cliffs and continue further around the edge of the map until you reach a large horseshoe-shaped bay. Fly up to the walkway of the buildings, using the cliffs to regenerate your Jetpack if need be. You should find the hidden marine up on these walkways. The achievement popped for me without ever actually seeing him/them.