A cheeky bit of strafe against a helo was always fun to practice. However, these days ASRAAM with helmet cuing would be the weapon of choice for a FJ, no need to worry about losing IR due to rotor downwash with that bad boy!
Oh, and even with less capable weapons there have been plenty of FJ vs Helo kills:
6 Feb 1991
USAF A-10A vs. IRAF Bo-105
A USAF A-10 ground attack aircraft shoots down an Iraqi Bo-105 helicopter using its GAU-8 30mm cannon.
7 Feb 1991 USN F-14 vs. IRAF Mi-8
A USN F-14 shoots down an IRAF Mi-8 helicopter with an AIM-9 missile. It is the last USN F-14 air-to-air kill
11 Feb 1991 USAF F-15Cs vs. IRAF helicopters
Two F-15Cs shoot down two unidentified Iraqi helicopters by using AIM-7 missiles for both.
14 Feb 1991 USAF F-15E vs. IRAF Hughes 500
An F-15E Strike Eagle fighter/bomber dropped a laser-guided bomb onto a Hughes 500 helicopter in the air. The helicopter was on the ground initially loading up commandos, though it took off. Even with it taking off they left the laser on it and the bomb hit it when it was "200 or so" feet in the air.
15 Feb 1991 USAF A-10A vs. IRAF Mi-8
An A-10A ground attack aircraft shoots down an Iraqi Mi-8 helicopter with its GAU-8 30mm cannon.
In 1978, a Soviet Mig-23 Flogger intercepted 4 Iranian CH-47 Chinook helicopters inside Soviet airspace, shooting one of them down and damaging another.
In 1988, two Soviet Mig-23 Floggers shot down a pair of Iranian AH-1J Super Cobra attack helicopters over western Afghanistan.
On 7 January 1992, an Italian Army Bell 206 helicopter was shot down by a Serbian MiG in Croatia.