The Falklands are interesting, because Argentina had Israel former III-C and Neshers - which had chopped arab aviations to bits twice, in the air and on the ground - except with guns and in clear weather. And rather close from home, Israel being so small...
Facing them were SHARs and at first glance they should have been chopped liver... even in dogfight and with guns, they may have suffered. In fact the Harrier had never been used as fighter, nor even created for that job. P.1154 maybe but not P.1127.
But they had a lethal weapon: the AIM-9L. Plus carrier decks nearby when Argentina was so far away. And that was more than enough to turn the odds against the Mirages (and smart Shackey Ward, too).
Israeli Mirages (even second-hand), may have been legends - but AIM-9L got the best of them and become a legend too.
On the first day of the war the Mirages came very high to save fuel and eventually beat the hell of the SHARs using their afterburners to a speed advantage.
The smart brits simply refused to fight, basically saying "So, what ? a Mirage at high altitude can't bomb the ships efficiently, so not a threat. So let's see how long you can loiter high there - we don't care."
The Argentinian pilots fell into the trap, got down to fight the SHARs or bomb the ships... and got kicked by the SHARs no longer at a disavantage.
(supersonic ? are you sure ? not at this height. Ah, wait, you have an afterburner and we have none.
Lesson 1 we don't need afterburner at low and medium height to beat you
Lesson 2 if you lit your AB and go supersonic, kiss goodbye to your return fuel.
But please, go ahead, make my day... lit your AB." )
What is noticeable is that the Argentinian pilots did not tried firing R-530 at short or medium range.
Bottom line: the missile was draggy even with only one carried on the centerline - in place of a big fuel tank; plus its efficiency was abysmal. So they didn't even tried.
And they had AIM-9s, too, but the antiquated AIM-9B with the stupid primitive seeker that locked on nothing or... everything but the ennemy exhaust.
In a sense, the first Mirage that got a radar good enough and a -530 good enough and in decent number (two) - was the Mirage F1C-200 with the Cyrano IV and two Super 530F under the wings. Still not a Phantom missile truck, but getting closer.
Mirage III with Cyrano II and 1*R-530 on the centerline was rather hopeless.
The Falklands war (merely a month before the Beka'a "turkey shot") is one of the first air war were missiles managed to shine.
(Vietnam I know had tons of AAMs fired - but reliability rates and kills were desperately low...)