How do you kill the zombies in the Royal Families' Tomb (third room)?

Do you mean the ReDeads?

ReDeads can be temporarily frozen by playing the Sun's Song. This also works on Gibdos. By freezing a ReDead it allows you to either escape saftely or to attack it mercilessly without having to worry about it's paralyzing scream (yes, that scream you hear is the ReDead).

ReDeads are blind. If you walk (or wear the Iron Boots) they will ignore you no matter how close to them you move. However, should you pull out an item they will hear you.

ReDeads are easily avoided, but can also easily be killed with the sword. Simply attack nonstop until it drops to the ground, pausing your assault for even a second will allow it to scream and latch onto you. Bombs also work nicely.

When you kill a ReDead something interesting happen. Its body does not dissapear or burn up right away. The corpse of the corpse remains for a while. During this time, it attracts any remaining ReDead in the area. If you kill one ReDead, the rest will slowly shuffle to the fallen one. They will ignore you until the body dissapears. This allows you to kill the rest of them extremely easily. (It is thought that either the "living" ReDeads are mourning the dead or are feasting on it's flesh).