You need to kill the Turkish beachhead of course, before the second wave of Turkish forces which was the one that brought armour ashore lands.
How to do this? If I am allowed to cheat give the Athens junta just a little bit of brains /paranoia. When they initiated the coup they either had or thought they had US assurances that Turkey would stay out of it as it was just an internal affair to remove the so called Castro of the Mediterranean from power.
Have someone with basic brains around. As soon as the coup happens, send out the Greek submarines to establish patrols off Cyprus (OTL they were ordered out on July 19th at about the same time with the Turkish landing force) and move the recently delivered F-4E to Crete (OTL moved after the crisis begun). For good measure airlift troops (one commando battalion per night) and use a pair of fast ferries (Rethymnon and Chanea) to land to Limassol a regimental combat team with armor. By the time Turkey can move the landing force is hit by the Type 209s and the Phantoms and any beachhead attacked by the Greek reinforcements. The Turkish Cypriot pockets can then be mopped up at leisure. Note that everything proposed above was within Greek military capabilities... and needs someone in the Greek general staff/government to actually have a coherent contingency plan beyond "we remove the Red priest whom our US friends also hate and want removed"
Option 2, without cheating. Replace the Greek commander on the spot, brigadier Georgitsis who to put it mildly did not prove up to snuff (and probably had a nervous breakdown) with someone more capable, colonel Kompokis head of Greek Cypriot commando forces for example as he's the second most senior officer in place. This in turn means the Cypriot National Guard opens up on the Turks as soon as they enter Cypriot territorial waters (Georgitsis waited... for explicit orders from Athens instead) and then applies the proper contingency plan (Afroditi 1, priority on the beachhead). Thus ELDYK along with the national guard armored units are used to hit in the night of 20 to 21 July the beachhead instead of hitting the heavily fortified Agyrta salient in broad daylight under Turkish air attack. Now OTL the beachhead was endangered by the far weaker Greek Cypriot counterattack that night. Throw the whole Greek strategic reserve at it and you have a fair chance of destroying it. If you do Greeks win. If not you are again at something close to OTL...