The girl was dead on arrival.
Following in the great tradition of bestowing characters with fanciful titles, usually in the form of "The Girl Who..." for the female characters, here we have The Impossible Girl Who Waited So Long That She Died.
The episode opens with the Doctor and Clara in some random trouble. Clara got a space boner that's lasted longer than four hours and needs to talk to the Doctor about it. So the Doctor smashes it, and everyone clutches their jewels a little tighter.
This is one of those things where the Doctor and Clara are caught up in something that is never explained outside of a sentence or two, but Clara's in a space suit because of it and that's all that matters. Ever wonder what would happen if they actually made an episode out of one of those one-line stories where the only part that matters is the tiny bit we catch at the end? Well, this episode is that.
The Doctor and Clara wander out of the TARDIS and are immediately captured by Vikings in horned helmets, because even though this has been repeatedly debunked and only exists in the first place due to the media inventing it as a short-hand method of representing Vikings... we're just gonna stick with short-hand methods of representing Vikings. One of the Vikings destroys the Doctor's sonic sunglasses right off the bat, then wears half of it as an eyepatch. Look, everyone, I'm Odin!
But then Actual Odin shows up, as a face in a cloud ala Monty Python. This is a British show, after all. Odin then sends down some prototype Judoon and beams up all the village's warriors to Valhalla. WITNESS ME!
Clara instructs one of the village girls how to use the sonic sunglasses to undo her manacles. Um... what's preventing Clara from doing this herself? Now that the sonic is hands-free, why does she need to instruct someone else how to use the glasses when she herself put the glasses on her face?
Monty Python God sees this use of advanced technology and beams Clara and the girl up, too. On the ship, Odin kills all the men and extracts all their man juices so that he can drink them, and yes, that is literally what he does. Clara thinks she and the other girl were spared because of their advanced technology, but it's obviously because they're significantly lacking in man juice.
The Viking girl declares war on the aliens because we were in need of someone doing something stupid to insert some means of conflict into this episode. Despite just seconds ago likening humans to mere cattle, Odin is for some reason enthralled at the prospect of waging war on them and sends Clara and the Viking girl back to prepare.
The Doctor first suggests just letting the aliens wipe out the village so they get bored and leave, but then he hears a baby crying and pretends it's saying something more poetic than "MEEEEE! MEEEEEE! PAY ATTENTION TO MEEEEEEE!" He uses this as incentive to train the remaining Vikings to fight, but they're all pathetic and nothing helps.
The Doctor goes and talks to the Viking girl, who starts making vague hints that she's "different" and this village is the only place where she's accepted, but goes into no detail about what exactly is "different" about her. This inspires the Doctor again, though, because he realizes something that everyone had overlooked.
That being that the village has barrels of electric eels.
Um... you do know that electric eels are indigenous to South America, right? I'd "overlook" the idea that a Viking village had electric eels the same way I'd overlook that they had kangaroos, ostriches, or pandas. And before someone trots out the usual excuse of "It's for kids, it doesn't need to be accurate", why in the world is that an excuse?
"Honey, this math book says 2+2=7"
"It's for kids, it doesn't need to be accurate."
"Honey, the latch on this car seat doesn't match the buckle."
"It's for kids, it doesn't need to be accurate."
"Honey, the prescription for our baby says it's for Viagra."
"It's for kids, it doesn't need to be accurate."
Why is it that writing is the one place where people stalwartly defend laziness under the excuse of it's okay to be lazy as long as a certain threshold of people won't notice it?
Whatever. The eels were pining for the fjords. Let's go with that.
So, using the eels, the Vikings construct the Giant Mouse of Minsk to scare away the aliens. Because if there's one thing "one of the greatest warrior races in the galaxy" is afraid of, it's a giant snake. And fart sounds.
With the aliens scared off surprisingly easily, everything is all happy. So... why is this episode titled "The Girl Who Died"? ... Ohhh, because by wiring the Viking girl into the alien helmet and having her project an image of a giant snake, she was exhausted and died. Way to spoil, title.
The Doctor starts ranting about how he's sick of losing people. ... Losing who? Ever since Moffat took over, very, VERY few people he's encountered have died for reals. Earlier in the episode he was afraid for Clara because she was the only person who mattered, but now the Viking girl matters, I guess? I'm not really sure what she did to leave an impression on him other than saying that she's "different" in some vague, undefined way.
The Doctor then flashes back to "The Fires of Pompeii" where Donna begged him to just save someone, and he saved Roman Capaldi. He realizes this is why he has Capaldi face now: to remind him to at least try to save someone.
So, the Doctor takes one of the alien's magic healy things and magically heals the Viking girl with it. Well, that was easy. Not sure what he was fretting about so much when that's all it took. Except now he's afraid he's accidentally made her immortal because the alien healy thing will continue to heal her forever, and she's going to be all alone.
... He does realize that he's already got someone who was brought back to life and accidentally made immortal, right? Just introduce her to Jack. But I guess his memory only goes as far back as series 4, minus "Journey's End" because everyone keeps forgetting that story happened.
This episode really struggled to find any kind of focus. It almost went out of its way to keep the Viking girl from having any definitive characterization other than being "different" and "coming up with stories", but these were both things that were merely mentioned rather than ever actively demonstrated. It was stretched out and looking for things to do for much longer than it needed to, all in the name of making it a two-parter. If anything, this episode probably could have sufficed as a single-parter and nothing of value would have been lost.