Hello all. My situation is this. I'm attacked by chewbacca, and I defend with the Devastator. The light side player wins the edge battle and strikes with chewbacca, dealing two damage to the Devastator. The Devastator then focuses to strike, but if it does it's combat damage to Chewbacca, Chewbacca retaliates double and kills the Devastator. So is possible to just assign the objective damage from the Devastator and not use the Unit damage? Or do you have to assign the damage to a target if there is one?

I will refer to you page 20 of the Rule Book, under step 5: Resolve Strikes. In the subheading called Resolving Strikes, it states

"To resolve a strike, a player follows these steps in order.

1. He chooses one of his participating ready units.

2. He focuses the unit to strike (i.e. places a focus token on the card).

3. He resolves the striking unit's combat icons by type."

There is no option within the rule book that allows you to not use specific combat icons if you wish to do so. Given that information I can only come to the conclusion that you must resolve all combat icons on your striking units.

yes you must use all combat icons, they are not optional.

Also, if you are defending you do not resolve objective damage icons on your units only the attacking player does. In your example, if the devastator was defending you could not have assigned objective damage from it.