We are the most real Greeks. Our dialect is the closest one to the ancient Greek and we decent from the original Greeks, the Achaeans (Mycenaeans). In mainland Greece they had more Greek tribes coming later on who pushed the Mycenaeans from the mainland to Cyprus. The Greeks in the mainland are therefore a mix of all Greek tribes while in Cyprus we are mostly the original Achaean Greeks.
Arcadocypriot Greek:
Arcadocypriot (Greek: Αρκαδοκυπριακή διάλεκτος) or southern Achaean (νότια Αχαϊκή) was an ancient Greek dialect spoken in Arcadia in the central Peloponnese and in Cyprus. Its resemblance to Mycenaean Greek, as it is known from the Linear B corpus, suggests that Arcadocypriot is its descendant. Proto-Arcadocypriot (~1200 BC) is supposed to have been spoken by Achaeans in the Peloponnese before the arrival of Dorians; for this, it is named also southern Achaean. The isoglosses of the Cypriot and Arcadian dialects testify that the Achaeans had settled in Cyprus.
The establishment happened before 1100 BC. With the arrival of Dorians in the Peloponnese, a part of the population moved to Cyprus and the rest was limited to the Arcadian mountains. After the collapse of the Mycenaean world, communication did not exist and Cypriot was differentiated from Arcadian. It was written up to the 3rd century BC with Cypriot syllabary.