Clara's death coming as a result of her becoming too much like the Doctor and taking a gamble in hopes of saving Rigsy and the Doctor's upset about not doing more to discourage her from emulating him accidentally carried the Aesop "Don't aspire to greatness or heroism" to at least one viewer who wrote to Doctor Who Magazine to complain about it. "Hell Bent" rectifies this interpretation somewhat by semi-reviving Clara, having her convince the Doctor to hold to his ideals instead of giving them up to be a Woobie, Destroyer of Worlds who thinks only of himself, and ending up with a TARDIS of her own so she can have adventures with Ashildr.
Since the people plotting against the Doctor — the Time Lords and Ashildr — are people the Doctor could have, respectively, killed (along with billions of innocents) or just let die instead of finding ways to save them, there's a nasty No Good Deed Goes Unpunished vibe throughout this three-parter.
It's either terrible that the episode killed Clara off... or it's great for killing her off.
The Doctor's rather forgiving attitude towards antagonists in this series, such as Bonnie the Zygon, made his fury at Ashildr for her role in Clara's death — he never would forgive her onscreen, though Clara would — a divisive topic. Did Ashildr deserve forgiveness, given that she didn't mean for anyone but the Doctor to suffer in the plot, or did her choice to betray him after all he did for her constitute a squandering of the second chance he gave her after "The Woman Who Lived"?
Ashildr really hit this hard for some fans, considering her HeelFace Revolving Door shtick and the fact she, by some variation, led Clara to her death. Also, even if she didn't mean for Clara to get hurt, she had no problem with betraying and hurting the man who saved her village and her life, who was willing to do anything he could to keep her from growing heartless — and couldn't even bring herself to apologize for it. Then again, did the Doctor "deserve" this for saving her life in a way that had unfortunate side effects — given that the alternative was not living up to his moral code and disregarding the lesson Donna taught him 'way back in "The Fires of Pompeii"?
Ending Fatigue: The climax, from the point where Clara reveals to the Doctor and Ashildr/Me that she has taken on the death sentence to her actual death. First the Doctor tries to force Ashildr to save her, then Clara gives two big speeches to the Doctor (one to talk him out of threatening others over her error, another to convince him to stay strong in his trials to come), and then her death takes place in slow motion, with several replays of the fatal moment from different angles. Death Is Dramatic, yes, but it's also dragged-out. Especially in light of later events that render her Only Mostly Dead, and which get their OWN dragged-out bits!
He's Just Hiding!: With two episodes left to go in Series 9, a significant portion of fans didn't honestly think Clara's Character Death was permanent, even though this was her departure season. As it turned out, while she was killed off in a Killed Off for Real way, "Hell Bent" reveals that she pulled from time at the very moment of her death, and exists as an immortal for a long time afterward before returning to that point. We still see her final death here.
Like You Would Really Do It: An unusual example: Clara actually does die in this episode in a way that leaves her Killed Off for Real, but there are fans who still thought this trope applied with two episodes left to go, claiming/hoping she'd be brought back to life in the finale.
Too Dumb to Live: Examined at face value, given everything she already knows about the chronolock and the Quantum Shade, it could be argued that Clara's decision to take the chronolock was a stupid decision on her part. Ashildr certainly thinks so, and with the power of hindsight, Clara wonders if she was subconsciously trying to get herself killed.
Unintentionally Unsympathetic: Ashildr/Me is theoretically sympathetic, as she's motivated to protect her community, and is clearly distraught about Clara's fate. The trouble is that she doesn't appear to care about the people of her community. Any crime is met with the death penalty, and she's apparently executed more than a few people in a very small population. She tries to justify it as the only way to keep the peace among aggressive alien species, but we see her execute a man for stealing town-owned medical supplies to save his dying wife. This means Ashildr could have saved that woman, but chose not to.