Aim at

The genitive is used with verbs signifying to aim at, strive after, desire (genitive of the end desired).

ἀνθρώπων στοχάζεσθαι to aim at men X. C. 1.6.29, ἐφῑέμενοι τῶν κερδῶν desiring gain T. 1.8, πάντες τῶν ἀγαθῶν ἐπιθῡμοῦσιν all men desire what is good P. R. 438a, τὸ ἐρᾶν τῶν καλῶν the passionate love of what is noble Aes. 1.137, πεινῶσι χρημάτων they are hungry for wealth X. S. 4. 36, πόλις ἐλευθερίᾱς διψήσᾱσα a state thirsting for freedom P. R. 562c. So with ὀϊστεύειν shoot at (poet.), λιλαίεσθαι desire (poet.), γλίχεσθαι desire. φιλεῖν love, ποθεῖν long for take the accusative.