According to Fazod and Bishop's seminal book on the Iran/Iraq war, there were a number of successful AIM-54 engagements. These included a (very unsporting) shot against a Super Frelon and, on a number of occaisions, multiple kills with one shot, due to the Iraqi predeliction for close formations and the warhead size of the Pheonix.
The F-14 had a VERY good war against the Iraqis, and successfully used AIM-9, AIM-7, AIM-54 and M61. They also flew with HAWK SAMs mounted on F14s. Oh, and the F4s had the then very Hush-Hush Combat Tree IFF fitted, and the "Zot Box" designator for LGBs.
There were lots of untrue reports circulated by the like of the US Navy; the combat reports appear to indicate, on the whole, a capable weapon system well employed.