This should be a new API module, since the existing systems for getting Wikibase entities won't be sufficient, and there are specialized needs for this particular type of entity. However, it should basically be wbgetentities except with only titles instead of the current ids|site&titles system.
Rough draft of an example API query:
action=wbgetmediainfo&titles=File:LighthouseinDublin.jpg|File:Foobar.jpg&languages=en|de&props=sitelinks|aliases|labels|descriptions|claims