Learn English – What does “leagues away” mean

I also hear "Also could you bring the file on the Rx accounts?" and the information you have provided is accurate.
The speaker is making a request. She is asking the secretary for the file "on Rx accounts". I also hear "Rx", but I am not convinced that this is correct. It might be some kind of special business lingo, a surname or a fake company name like "Arix Company".

Anyway, the file on X accounts means the file regarding/about X or the file that contains the transactions with X. In X accounts, X is a noun that modifies accounts. So, the file on Rx accounts likely means the file with the transactions regarding prescriptions. Maybe the speaker runs a pharmaceutical company, for example. If we pretend it's a company name or surname "Arix", then Arix accounts would be accounts regarding the transactions the speaker makes with Mr./Mrs. Arix (or the Arix Company). Think of "Smith" if "Arix" doesn't make sense.

As was pointed out on that other question you linked, this is a surprisingly tricky sentence!

Let's slowly build it up.

It will take someone else.

What is "it"? Stopping Voldemort again. Implied but never directly said. As for "take", we could say "need" instead, just to be slightly clearer.

[Stopping Voldemort again] will [need] someone else.

This isn't "someone else" as in "we need a different person", but as in "we need other people prepared to do what you did, Harry". When will they be needed? "Next time" (that is, the next time that Voldemort tries to return).

[Stopping Voldemort again] will [need] someone else who is prepared to [do the same as Harry] next time.

Now, Dumbledore is saying that this someone else doesn't have to do much. Hence, it will "merely" (or "only") take someone else. This may sound like it's demeaning Harry's efforts, but it's meant to be reassuring Harry: standing up to Voldemort is not very difficult or unlikely after all, and it doesn't take someone extra-special to do it.

[Stopping Voldemort again] will merely [need] someone else who is prepared to [do the same as Harry] next time.

What, exactly, did Harry do that Dumbledore says they need other people to do (or be prepared to do)? "Fight a losing battle"--or what seems like a losing battle. (Dumbledore omits the word "like", but I'll leave it in for this one example.)

[Stopping Voldemort again] will merely [need] someone else who is prepared to fight a losing battle next time.

[Stopping Voldemort again] will merely [need] someone else who is prepared to fight what seems [like] a losing battle next time.

And now we just replace the bracketed bits with the different wording Dumbledore uses, and we have the sentence (okay, part of a sentence) that you bolded.

It will merely take someone else who is prepared to fight what seems a losing battle next time.