To start with, there's Hiro-chan's arc. Watching her break down just after the test tube incident, unable to cope with any more suffering hurts. So does Hoshimaru being forced to kill Hiro-chan to save Shiina's father, traumatising Shiina in the process, which the anime version manages to make even sadder by having Hiro-chan shed one more tear just as she dies. Actually, the whole arc is pretty harrowing. Poor, poor Hiro-chan.
This troper found the chapter about Shiina's first day of middle school to be really sad, but in a semi-heartwarming way. When Shiina fills up the tub and asks her dad if they can take a bath together, like they used to, and he says that they can't, it's already sad enough. But what really made me tear up was the next page, with Shiina crying and telling him that she wants to be his "little Shiina" one last time.
The last three volumes have too many tearjerker moments to count, but one of the most memorable and scarring is Shiina's death near the end of volume 10. Seeing the beloved character literally cut in half by Vulcan rounds just after the insinuation that she might not be the main character after all is all but guaranteed to leave an impression, even on readers who aren't the crying type. That death scene and the words Returning Home in a Bag may well permanently burn themselves into your mind.
Volume 11 begins with an extremely miserable chapter - which, as it so happens, is directly related to the above two moments. You know the rest of the volume isn't going to be much happier when, not too long afterwards, Takeo of all people starts crying.
Perhaps one of the hardest-hitting moments of all comes in chapter 65, just two chapters short of the end, which has Shiina going into a severestate of denial over the death of her father, to the point where she says that she'd like to go home and have dinner with her dad and Akira, and perhaps invite Hiro-chan too. When you remember that Hiro-chan died six volumes ago, it's absolutely heartbreaking to read. Right after that Akira, wounded and in tears herself, begs Shiina to come to her senses and make peace with her mother, the last family Shiina has remaining... and finally, just to twist the knife even further, a few pages later there's final images of deceased characters like Hiro-chan and Norio. God. Damn. You. Kitoh.