The majority of achievements are unmissable and are automatically given as you read the VN. Still it may be helpful to know which ones you definitely won't miss.
Missable ones are given ONLY during Episode 8 for endings and for correctly solving the puzzles and mysteries. I'd recommend to try and solve them yourself as that is more fun (even by trial and order), but I will provide the solutions anyway. I recommend to save beforehand.

These are given automatically after episode completion and at various other points during the VN.

These achievements are given during Episode 8 and can be missed, but you can reload the save later and still get them.

These are given for successfully completing the minigames in Episode 8.
Achievement is given after solving all puzzles during the party and getting every medal. You can solve them yourself, most of them are pretty simple especially with hints, and you can save and reload if you make a mistake. Here are the answers:
1 - A
2 - A
3 - B
4 - D
5 - C
6 - D
7 - E
8 - A
9 - D
10 - C
11 - D
12 - E
13 - A
14 - C
15 - E
16 - C
This achievement is given for succesfully solving Bernkastel's mystery without any hints. Again, save beforehand if you want to try it yourself, it's pretty complicated, but solvable. If you're struggling you can go through the hints and then reload your save, but if you're REALLY struggling or don't care about solving mysteries the answer is Rudolf, Kyrie and Battler.

These are given for different endings in Episode 8. Both are pretty close to the end of the game. I recommend saving when you finally see the golden door and starting with Ending A as it's shorter and (sort of) less impactful.
For this achievement pick the "Trick" option.
For this achievement pick the "Magic" option.

Given for getting all other achievements