Assuming a compound with ἀντι- (anti-, “opposite, against”) does not help much; the connection with ἀντικρούω (antikroúō, “to come into collision”), suggested by Kretschmer, is improbable, as are other attempts, like a derivation from ἀντι- (anti-, “against”) +‎ κάρα (kára, “head”). Beekes and Cuypers argue that the -υ is short, but metrically lengthened in Homer. Beekes does not exclude a Pre-Greek etymology.

ἀντικρῡ́ • (antikrū́)

1. face to face, over against
2. straight on
3. outright

• “ἀντικρύ”, in Liddell & Scott (1940) A Greek–English Lexicon, Oxford: Clarendon Press
• ἀντικρύ in Cunliffe, Richard J. (1924) A Lexicon of the Homeric Dialect: Expanded Edition, Norman: University of Oklahoma Press, published 1963
• ἀντικρύ in the Diccionario Griego–Español en línea (2006–2025)
• Beekes, Robert S. P. (2010) “ἀντικρύ”, in Etymological Dictionary of Greek (Leiden Indo-European Etymological Dictionary Series; 10), with the assistance of Lucien van Beek, Leiden, Boston: Brill, →ISBN, page 109