Does Nyssa need to face The Master?

No

Really, she didn't like recording Companion Chronicles?

Isn't the 5th Doctor episode of The Destiny of the Doctor a Master story?

Nyssa does already have several Master stories on record though:

TV - The Keeper of Traken, Logopolis, Castrovalva, and Time-Flight
Big Finish - Smoke and Mirrors (Destiny of the Doctor), The Toy (Short Trips), and The Light at the End

What in particular are you looking for here, because even if you mean post-Castrovalva (it's all one on-going adventure for her until then), she's still got 4 stories with him after that, one of which even happened onscreen.


EDIT: Additionally, it wouldn't make sense for her to meet, properly, in person, any other incarnation than Ainley's, so I'm not really sure how another story could be adequately told. (I know you suggest Short Trips, but I don't know if that sort of story could be adequately told in that format; they've also already done The Toy and any other story would seem too similar for Big Finish to want to try it)

I remember reading somewhere she really didn't enjoy the experience back in 2008. But, obviously given The Toy and A Heart on Both Sides, she's changed her mind since then

I don't know if Nyssa actually needs to face The Master, but it could certainly make for a powerful story, and I think a one-hander like a Short Trip might be very good since there's a particular poignancy to it being Ainley's unavailable Master. It's part of why I take his version of the Master very seriously after what he did to Tremas and to Traken and etc - and after all that, if he turns up again it's going to be the image of Tremas staring her right in the face, just to twist the knife. That's some pretty nasty stuff, and no doubt it leaves her with some difficult issues to work through.

I keep daydreaming about a 3 box-set limited series, Traken* in which Nyssa tries to figure out how to undo some of the damage the Ainley Master has done - in the opening story, 1.01 The Opposite of Entropy, Nyssa invents an Entropic Inverter in order to further stabilize E-Space, which incidentally also allows her free passage to and from E-Space, and reverts her to her TV era screen age**. She slowly realizes that she may have inadvertently created the means to restore her homeworld. (In the second story, she starts seeking out survivors or descendants of Traken so that they might participate in making the fateful decision whether or not to attempt Traken's restoration. Naturally the Time Lords don't want anyone to have their hands on such a powerful thing, and there is a particular villain (one guess who) who detects its curious emanations and cannot wait to get their hands on it. (If Nyssa succeeds, eventually she will have to face a number of other difficult decisions, including whether or not she will become the new Keeper of Traken).

Naturally, since I'm only daydreaming there will be tons of guest appearances in the series (the story demands this), including Nyssa's son having the opportunity to meet his namesake, and an alliance formed between Traken and Trion, with the latter under the rule of one Turlough. (As the apparent originator of these ideas, I hereby declare them to be in the public domain, and free for Big Finish to use just as freely as if HG Wells had come up with them).

Never mind me, I've probably had several jelly babies too many today, but I love the idea of something like this*** and it's been very hard for me to get over daydreaming about it. I think it was only a couple weeks ago I finally actually started into my first really weak attempt at mocking up the first cover, before deciding I just don't have the graphic skills for it.

(*Traken Series: 1. Traken Remembered, 2. Traken Reborn, 3. Traken Rising)
(**I know, we can't just have characters who keep regenerating just so they can be in more stories... Oh wait...)
(***I think this actually started as my response to complaints about Nyssa being in too many MR stories, so it did kind of seem like a good thing to do at the time).