You have to get all 8 specialist weapons in zombies to level 3.
There are 4 weapons on the chaos side, 4 on the aether side. There’s no in game tracker so you have to remember which ones you got to level 3.
Getting them to level 3 is easy. It takes about 6-7 uses of each weapon, I was averaging 15 rounds per specialist weapon. There is a number next to the weapon in the bottom right corner, that’s how you can tell what level it is at. Your best bet is to wait until you have a full horde before using your specialist. Fastest mode to do this in is rush, but not necessary.
If only aiming for this achievement, it will probably take 4 hours.
You don’t need to use the weapon after it turns level 3, so you can quit out afterwards if you’d like
As dizzy mentioned in the comments, you could use the supercharged crystal talisman and it will still count