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That is just a bunch of layers (images) tied to a null or pre-composed. You can collapse transformations and apply wiggle to position and rotation in a nested comp (pre-comp) or parent all off the background layers to a null and animate or wiggle the position and rotation of the null.
This is really basic stuff. Are you new to AE? If so, please spend some time in the Learn workspace and with the User Guide. A couple of hours there will save you days of poking around trying to guess how After Effects works.