Overwatch 2

About the game mode
This achievement is exclusive to the Winter Wonderland event in december (every year). Might turn up in the Anniversary event (different random events every day in May). It can be found in the Arcade menu, it is the 8 player FFA mode not the 6v6.

Rules of snowball fight
Everyone plays Mei who has her wall and ice cube abilities from the main game. However she can only shoot icicles with a limited range and ammunition. One hit kills, the one who gets 15 kills first wins the game. Every player starts with 1 ammo and can get more by picking up (hold or ) piles of snow randomly appearing on the map (max 3). There is an important new ability by pressing the melee button : if someone shoots at you and you activate melee you can grab the icicle in the air and load it into your weapon. The ultimate attack is different as well: for a few seconds you can shoot as many icicles as you want with a greater speed. After the ultimate ends your weapon will be fully loaded with 3 ammo as well.

The achievement
You start with 1 ammo. Pick up 2 more right away, then you have to kill 3 people without dying or picking up more ammo. Catching icicles is reloading so don't use melee. DoctorWho426 confirmed you can catch icicles and use those as ammo without voiding the achievement. Easiest way to ensure you won't miss is sneaking up on people who are picking up ammo or shooting at each other. The ultimate ability may work for this but I did it with normal shots and can't confirm it.
AES0P and Dixxxxxon confirmed you can use your ultimate to get the achievement, you can even start with normal shot kills then finish it with the ult.
The ultimate reloads your weapon when it ends so you have to get the third kill before.
If you are sure you should've gotten the achievement but it isn't unlocking then follow the advice of Kroni: Press the Guide button, go to achievements and select "See all my achievements" then select Overwatch. Any stuck achievement should unlock in the game.