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The collectibles on this map are in the form of snow globes. Shoot 10 to unlock this achievement. They are not available all at once. As you complete waves, you open up areas that were previously inaccessible. Therefore, while you cannot get all 10 snow globes with the strategy of leaving one Zed alive, you can do this at the end of each wave until all collectibles for that area have been obtained.

Each new area has 3-5 collectibles and depending on the length of the game being played will determine how soon you can unlock this. For instance, if you play a Short (4 wave) game, you can unlock this by Wave 3. A Medium (7 wave) game can unlock this by Wave 4. And finally, for a Long (10 wave) game, this can unlock by Wave 5.

The reason for this is that if you play a longer game, a new area does not open up after every wave. The longer the game, the more you have to clear waves in the same area.