"She remembers the happy days."
Translation:Ŝi memoras la feliĉajn tagojn.
Why does the accusative apply to remembering something? Isn't this typically for actions?
It's used for the objects of pretty much all verbs, including things such as "have" or "remember".
About the only ones that have a complement rather than an object (and so don't use accusative) are things such as "be" and "become".
That would be "joys".
Perhaps you mean "ĝojajn" instead? That would be "joyful".