this came up last night during a game and while we made a spur of the moment table ruling, my group and i were curious about something more official.  is it manadatory to focus a unit if they only have edge dependent icons and you did not win the edge battle. Case in point "Guardian of Peace" has only one unit damage icon that is edge dependent.  if she is defending, for instance, and i did not win the edge battle, she obviously cannot strike in any way, so does that still neccesitate placing a focus token on her?

Yes, you still focus them.  There is a diagram on page 26 that walks you through strike resolution. Step 6 shows the last unit in the engagement as having edge dependent icons, and that player lost the edge, and they show that unit being focuses to strike even though it can't.

Yes they must be focused.

Page 20

A player does not have the option to pass during this
step. If he has at least one ready participating unit, it
must focus to strike.

Page 23

After all units participating in the engagement are
exhausted (either by striking, by receiving a focus token
during a ∫ icon resolution, or by other card effects), the
resolve strikes step is over.

A good example of this could be using R2DS to attack and then using Target of Opportunity to deal 1 damage to an objective.  While R2 can't deal any damage, if you didn't attack with him you couldn't play TofO.  Therefore he should still have to focus as he participates.

If R2-D2 is unopposed he would get the unopposed damage bonus as well.