Question :

If an opponent has the " Protected " card assigned to their figure -and- my figure hits using the attack power " Precision Strike " , does my opponents' figure ignore all of the damage ?

Protected ignores damage. It does not reduce it. Since it doesn't reduce it, Precision Strike doesn't do anything. The figure would take no damage

Ignoring damage is not the same as reducing it so Protected will be able to ignore the whole damage.

It always helps to include the relevant text of what your question is about:

Protected:

Notice how "ignored" is not one of the things that Precision Strike prevents?

Therefore, Protected would ignore the Precision Strike attack and in its place, an action token would be placed on the hit figure and the opponent would score 8 Victory Points (for the Protected).

Hope that helps.

Edit: Beaten to the punch...