In the case that you guys don't know, you CAN get the M60 in survival. Just go to Survival, pick The Passing, chose the second option. Exactly where you spawn, there are some Boomer Biles and an M60. Then just start the game, throw the Boomer Bile and as soon as you see the Horde Come, fire away, you can even kill all your team mates to make sure they don't kill any of the horde if you want.
Also; This achievement might be glitched, you might get it by only killing 10, or 5, or you might end up having to kill all 25. I got it by only killing 13.
Edit:Thanks to Casey Da Gr8 1 for pointing this out, there are also Explosive Rounds, you can use that to kill zombie's even faster, and make the achievement easier!
Edit: This also works on the first Survival map for the Passing.