As pointed out by Cairnarvon (see his/her comment above and the useful link), this seems to be a Greek accusative, which is also referred to as "accusative of respect" (see cmw's comment below and related questions: question1 and question2). The following relevant information/confirmation can be found here:
"Ennius in his Annals ventured on this Accusative in v. 311 V. perculsi pectora Poeni, and found imitators in subsequent Dactylic poets (e.g. Lucr. 1, 12 perculsae corda tua vi). It is probably a Graecism"
(Source: Syntax of Plautus. W. M. Lindsay. Anne Mahoney. edited for Perseus. Oxford. J. Parker and Co. 1907).
As for your Latin sentence, please note that it is aeriae (not aeria), which agrees with volucres (Nom.pl.fem). Your English translation is ok to me. As for your comment "I would expect (...) ad or in e.g. perculsae ad corda", it seems to me that your natural expectation/intuition can be due to a matter of (the translation to) our languages, which lack this peculiar construction. As you correctly point out, a preposition(al expression) is often needed when translating this peculiar accusative to our languages.
More detailed information on this construction can be found in Pinkster's (2015: 242-245) Oxford Latin Syntax (vol. 1). The following text is an excerpt of his Section "5.7 Accusative constituents with true passive forms":
True passive verb forms (passive participles much more often than finite forms) can be combined with accusative constituents. Their syntactic status is much disputed. In corresponding active expressions they usually function as object, but in the passive they seem to be optional. The phenomenon is almost confined to poetry. It is relatively common with verbs of hitting, wounding, binding with the (usually human) patient as the subject and the part (of the body) in the accusative, but it occurs with other classes of verbs as well. Imitation of semantically similar Greek constructions or extension of the possibilities of Latin is very likely.
The oldest example (if genuine) of a passive participle of a verb of hitting in combination with an accusative constituent is (a). The earliest attested prose example is (b).
(a) perculsi pectora Poeni ...
(‘...the Carthaginians were stricken in their hearts...’ Enn. Ann. 311V=310S)
(b) Dedecores inultique terga ab hostibus caedebantur.
(‘Disgraced and unavenged, they were struck in the back by the enemy.’
Sal. Hist. frg. 3.24)
(c) ...nova proles / artubus infirmis teneras lasciva per herbas / ludit lacte mero mentes perculsa novellas. (‘Through this a new brood with tottering legs sports wanton among the soft grass, their baby hearts thrilling with the pure milk.’ Lucr. 1.259–61—tr. Bailey)
(d) At te, Nesse ferox, eiusdem virginis ardor / perdiderat volucri traiectum terga sagitta. (‘But, O savage Nessus, a passion for the same maiden utterly destroyed you, pierced through the body by a flying arrow.’ Ov. Met. 9.101–2)
(e) (sc. Hector) aterque cruento / pulvere perque pedes traiectus lora tumentis. (‘...black with gory dust, pierced with thongs through his swollen feet.’ Verg. A. 2.272–3).