Almost nobody works as a "Latin translator" per se. Of course, it does depend on what is getting translated and why, but this isn't really a career that exists.

Presuming we mean primarily Latin or Ancient Greek, most of those involved in doing translation are researchers and professors - they are academic staff employed to do research, who produce translations as part of their work, not the primary output of their work.

That means (a) a PhD is a minimum to get into such work, (b) usually in Classics, but depending on where you are and what your specialty is, Ancient History might be your umbrella discipline; rarely linguistics (specialists in linguistics of ancient language exist, but they are not normally doing a lot of translation).

The job market for classics PhDs, like all humanities PhDs, is pretty bad at the moment and unlikely to improve any time soon. So getting an academic position that allows you the time, money, and contacts to do translation is difficult.

The reason why I said earlier that it's mainly academics who do this work, is that while anyone can translate anything, producing a translation for market mainly revolves around (a) having credentials to get it turned into an academic book (b) having that book serve a broader academic market to some extent. Translation itself is (unfortunately!) not as highly esteemed in the academic gain as, say, original research based on texts. So doing only translation doesn't get you very far career wise.

That's my take on it, some others in similar fields might have their own to add.

No, the Vatican is not really a big market for translators. (Yes, they have some, but it's unlikely to ever be you).