There has been some debate about what counts for this achievement and what not. Since the Metro Wiki displays the most tested theory I will use their findings for this guide.
Hints & Notes:
- Stashes consist of places with boxes/safes with items inside or wooden crates with items on them.
- You don't have to interact with the stashes in any way. Approaching them is enough. This includes locked safes.
- There's no in-game feedback for finding a stash. It's a hidden mechanic.
- Loading checkpoints is OK, but your progress will be reverted to what is was at the time of the checkpoint.
- Dead bodies are not stashes.
- Items just laying on the floor are not stashes.
There are 12 stashes in total:
1. Orange box in the starting terminal. First floor, just after the stairs.
2. Safe in the starting terminal. First floor, in a room at the end.
3. Safe in the second building. Ground floor. Stand with your back to the stairwell, then follow the right wall.
4. Stash with a Tihar in the second building. First floor, accessible through an elevator shaft in the second floor.
5. Crate with items on top, inside the back of a truck. To your left just before you can see the playground.
6. Indoors camp with a lit bonfire. Accessible through a window just before entering the playground.
7. Green box in the building after the playground. Follow the right wall after entering the building.
8. Red box inside the back of a truck in the flooded intersection. Requires jumping over the water off of a submerged car. (Part of the car is underwater but can still be walked on.)
9. Orange box inside a minivan. Pass the flooded intersection, climb the stairs and turn around.
10. Stash with tape message from Hunter. Inside the building after the flooded intersection, in a room at the end of a hallway with two traps.
11. Orange box behind a crack on the wall. Follow the left wall after the drop in the stairwell and you'll eventually find it. The place is irradiated and there's a grenade tripwire.
12. Building marked with a stencil with a Safe inside. Shortly after reuniting with Bourbon, he'll lead you up some stairs and into a fight. Instead of following him upstairs, turn around and follow the wall to your left. The achievement/trophy should trigger after getting through the window.
This video only shows the 12 mentioned stashes:
If you want to be really safe you can follow this video where basically every piece of ammo is picked up: