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Tear Jerker: Hell Boy
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In "The Wolves of Saint August". The panel in which the young girl transforms into a werewolf in front of Kate Corrigan... (shudders).
The death of Vasilisa The Beautiful by Koschei The Deathless. Not only the fact that she is just a little girl that packs the punch, but the Baba Yaga is forcing Koschei into killing Hellboy by offering his own death in exchange... Koschei dies no less than three times in pursuit of Hellboy, all the while he is begging the Baba Yaga to just let him die with some dignity.
The death of Hellboy, of course.
In the same story line, when Hellboy finds that Alice has died, charred by flames that wouldn't kill him, but would kill a normal person in no time. Turns out it was only an illusion, but damn!
Mike Mignola really has a thing against gorillas and chimps. They always get killed in very creative ways... and they always cry for help... sometimes with a human voice. (sob)
In Hellboy's sister publication B.P.R.D., the death of Roger The Homunculus.
Professor Broom's death. He would have died anyway but still, Red wasn't ready yet. The worst may be that it was inevitable.
When Rasputin sucks out Liz' soul while Hellboy is bound in an unbreakable shackle. He is in sheer anguish. Not being there to stop his father being killed is bad enough, but it's worse when you are there, but can't do anything to stop it.
The Golden Army
The forest god's death is very bittersweet, specifically the music that they played during the scene.