Learn Hardcore Arabic (Levantine): هي طلعت مع امي ورجعت عالبيت. - She went out with my mother and returned home.

Because the subject is هي = she, and in Levantine Arabic the 3rd person feminine singular in the past tense usually ends in -et / -it / -at, depending on pronunciation.

So:

طلع = he went out / he came up
طلعت = she went out
رجع = he returned
رجعت = she returned

That -ت is one of the main clues that the subject is feminine singular in the past.

Do I need to say هي, or could I just say طلعت مع امي ورجعت عالبيت?

Yes, you could leave out هي.

In everyday Levantine, subject pronouns are often dropped when the verb already makes the subject clear. Since طلعت and رجعت already show she, the sentence still works without هي:

طلعت مع امي ورجعت عالبيت
= She went out with my mother and came back home.

Including هي adds a bit of emphasis or clarity, especially if you are contrasting her with someone else.

What exactly does طلعت mean here? I thought it meant went up or came out.