You can check your progress from the start menu. Diaries save upon collecting them so you can quit out to the main menu after grabbing a diary if you might have missed one.
The Metro Wiki has a nice written guide for all the diary's:
https://metrovideogame.fandom.com/wiki/Artyom%27s_Journal_(M...)
Alternatively you can use this more in dept guide for more of a total walkthrough style:
https://gamefaqs.gamespot.com/xboxone/824052-metro-2033-redu...If you prefer a video guide which I would highly recommend for this achievement then I would go with this one: