2 achievements are missable. The first one requires completing all of Monika's events. Unlike other characters, some of Monika's events have time limits and thus can be failed. The time limits are very obvious however, just do what she says, she means it. The second missable achievement is tricky, you need to craft a Philosopher's Stone BEFORE beating the final boss. If you manage to do it, you'll see a special cutscene where Sophie discovers a new power. But you won't get any achievement just yet. Beat the final boss, and one more achievement will pop up during the post-boss cutscenes.

Originally posted by iriyap:

2 achievements are missable. The first one requires completing all of Monika's events. Unlike other characters, some of Monika's events have time limits and thus can be failed. The time limits are very obvious however, just do what she says, she means it. The second missable achievement is tricky, you need to craft a Philosopher's Stone BEFORE beating the final boss. If you manage to do it, you'll see a special cutscene where Sophie discovers a new power. But you won't get any achievement just yet. Beat the final boss, and one more achievement will pop up during the post-boss cutscenes.

...So regarding Monika, I did the first time limit event of hers, but now her friend level is stuck at 45 and I don't know how to trigger her next event.