In the scene where a lion tries to attack David's sheep, there are moments that could be quite scary.
There are two battle scenes which have some scary moments.
Amalekites are somewhat scary in appearance, resembling witch doctors or some sort of tribal creature.
When David first comes to the palace, Saul is in a rage (controlled by his demon/demons) and some loud crashing can be heard but not exactly seen which may be a bit scary for some viewers and loud depending on the device and volume of the device.