Complex sentence: The 2nd Parachute Battalion advanced on the southern route along the river, above them 3rd Parachute Battalion took the Heelsum-Arnhem road through Oosterbeek, while the 1st Parachute Battalion initially remained in reserve with brigade headquarters.
Split into simpler sentences: The 2nd Parachute Battalion, along the southern route along the river, above them 3rd Parachute Battalion on the Heelsum-Arnhem road through Oosterbeek. While the 1st Parachute Battalion initially remained in reserve with brigade headquarters.