This page of the Metro Exodus Two Columns guide shows a description of all the achievements (trophies).
New Year - Bronze Trophy
How to unlock: Celebrate The New Year.
Commentary: You get this achievement/trophy by progressing through the game - when the General makes a New Year speech.
Duty and Conscience - Bronze Trophy
How to unlock: Make a moral choice in the chapter.
Commentary: You need to make a choice regarding the medicine. The choice doesn't matter, you will always get this trophy.
Father and Son - Bronze Trophy
How to unlock: Provide guidance for Kirill.
Commentary: You get this achievement/trophy by progressing through the game - right before you go down to the bunker.
Real Colonel - Gold Trophy
How to unlock: Complete the expansion.
Commentary: You unlock this achievement/trophy by completing the DLC.
The whole picture - Bronze Trophy
How to unlock: Find 9 hidden diary pages.
Commentary: A walkthrough for this achievement/trophy can be found on a separate page of this guide.
Mind you, it's quite heavy! - Bronze Trophy
How to unlock: Kill 3 Nosalises with flamethrower's melee attack.
Commentary: You must hit and kill 3 Nosalises with the flamethrower's melee attack.
Dodge master - Bronze Trophy
How to unlock: Dodge all of the Blind One's throwing attacks.
Commentary: You encounter the Blind One at the end of the expansion. The gorilla will throw objects at you - avoid attacks and burn the creature with a flamethrower.
It's just a scratch - Bronze Trophy
How to unlock: Complete the DLC without using first aid kits, at least on the normal difficulty level.
Commentary: You can't heal yourself throughout the entire DLC, but you can die and load the game - use this to get the trophy/achievement.