The tough foreign policy of Bush Administration damaged/hurt the relationship betwen the US and its European allies, causing the US international reputation to plummet/fall off a cliff/plunge.
The tough foreign policy of Bush Administration damaged/hurt the relationship betwen the US and its European allies, and the US international reputation plummeted/fell off a cliff/plunged/was tarnished/was in tatters.
The tough foreign policy of Bush Administration damaged/hurt the relationship betwen the US and its European allies, causing the rapid fall/degradation/decline of the US international reputation.